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Journal articles on the topic 'Multiplicative operator'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

XU, Z. S. "EOWA AND EOWG OPERATORS FOR AGGREGATING LINGUISTIC LABELS BASED ON LINGUISTIC PREFERENCE RELATIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12, no. 06 (2004): 791–810. http://dx.doi.org/10.1142/s0218488504003211.

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In this paper, we define two types of linguistic preference relations (multiplicative linguistic preference relation and additive linguistic preference relation), and study some of their desirable properties. We introduce the extended geometric mean (EGM) operator, extended arithmetical averaging (EAA) operator, extended ordered weighted averaging (EOWA) operator and extended ordered weighted geometric (EOWG) operator. An approach based on the EGM and EOWG operators and multiplicative linguistic preference relations and an approach based on the EAA and EOWA operators and additive linguistic pr

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2

Avsyankin, Oleg Gennadievich, and Alisa Markovna Koval’chuk. "Multiplicative Discrete Convolution Operators with Complex Conjugate Operator." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 2 (2016): 17–21. http://dx.doi.org/10.18522/0321-3005-2016-2-17-21.

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3

Gulsen, Tuba, Sertac Goktas, Thabet Abdeljawad, and Yusuf Gurefe. "Sturm-Liouville problem in multiplicative fractional calculus." AIMS Mathematics 9, no. 8 (2024): 22794–812. http://dx.doi.org/10.3934/math.20241109.

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<p>Multiplicative calculus, or geometric calculus, is an alternative to classical calculus that relies on division and multiplication as opposed to addition and subtraction, which are the basic operations of classical calculus. It offers a geometric interpretation that is especially helpful for simulating systems that degrade or expand exponentially. Multiplicative calculus may be extended to fractional orders, much as classical calculus, which enables the analysis of systems having fractional scaling properties. So, in this paper, the well-known Sturm-Liouville problem in fractional cal

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4

XU, YEJUN, and HUIMIN WANG. "POWER GEOMETRIC OPERATORS FOR GROUP DECISION MAKING UNDER MULTIPLICATIVE LINGUISTIC PREFERENCE RELATIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 20, no. 01 (2012): 139–59. http://dx.doi.org/10.1142/s0218488512500079.

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The aim of this paper is to develop some new linguistic aggregation operators, such as linguistic power geometric (LPG) operator, linguistic weighted PG operator, LPOWG operator which are based on PG operator. We have studied some desired properties of the developed operators, such as commutativity, idempotency, boundary, etc. Moreover, we have developed two approaches to deal with group decision making problems under multiplicative linguistic preference relations. If the weighting vector of the decision makers is known, we develop an approach which is based on the linguistic weighted PG opera

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5

Lu, Fangyan. "Multiplicative mappings of operator algebras." Linear Algebra and its Applications 347, no. 1-3 (2002): 283–91. http://dx.doi.org/10.1016/s0024-3795(01)00560-2.

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Gong, Zhiwei, Jian Lin, and Ling Weng. "A Novel Approach for Multiplicative Linguistic Group Decision Making Based on Symmetrical Linguistic Chi-Square Deviation and VIKOR Method." Symmetry 14, no. 1 (2022): 136. http://dx.doi.org/10.3390/sym14010136.

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Most linguistic-based approaches to multi-attribute group decision making (MAGDM) use symmetric, uniformly distributed sets of additive linguistic terms to express the opinions of decision makers. However, in reality, there are also some problems that require the use of asymmetric, uneven, i.e., non-equilibrium, multiplicative linguistic term sets to express the evaluation. The purpose of this paper is to propose a new approach to MAGDM under multiplicative linguistic information. The aggregation of linguistic data is an important component in MAGDM. To solve this problem, we define a chi-squa

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7

Thaheem, A. B., and A. R. Khan. "On some properties of Banach operators. II." International Journal of Mathematics and Mathematical Sciences 2004, no. 47 (2004): 2513–15. http://dx.doi.org/10.1155/s0161171204309233.

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Using the notion of a Banach operator, wehave obtained a decompositional property of aHilbert space, and the equality of two invertible boundedlinear multiplicative operators on a normed algebra with identity.

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8

Dragomir, Sever S. "Multiplicative inequalities for weighted arithmetic and harmonic operator means." Acta Universitatis Sapientiae, Mathematica 11, no. 1 (2019): 54–65. http://dx.doi.org/10.2478/ausm-2019-0005.

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Abstract In this paper we establish some multiplicative inequalities for weighted arithmetic and harmonic operator means under various assumption for the positive invertible operators A, B. Some applications when A, B are bounded above and below by positive constants are given as well.

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9

Hebestreit, Fabian, and Steffen Sagave. "Homotopical and operator algebraic twisted K-theory." Mathematische Annalen 378, no. 3-4 (2020): 1021–59. http://dx.doi.org/10.1007/s00208-020-02066-6.

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Abstract Using the framework for multiplicative parametrized homotopy theory introduced in joint work with C. Schlichtkrull, we produce a multiplicative comparison between the homotopical and operator algebraic constructions of twisted K-theory, both in the real and complex case. We also improve several comparison results about twisted K-theory of $$C^*$$ C ∗ -algebras to include multiplicative structures. Our results can also be interpreted in the $$\infty $$ ∞ -categorical setup for parametrized spectra.

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10

Kluvánek, Igor. "Scalar operators and integration." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 45, no. 3 (1988): 401–20. http://dx.doi.org/10.1017/s1446788700031116.

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AbstractThe notion of a scalar operator on a Banach space, in the sense of N. Dunford, is widened so as to cover those operators which can be approximated in the operator norm by linear combinations of disjoint values of an additive and multiplicative operator valued set function, P, on an algebra of sets in a space Ω such that P(Ω) = I, subject to some conditions guaranteeing that this definition is unambiguous. An operator T turns out to be scalar in this sense, if and only if, there exists a (not necessarily bounded) Boolean algebra of bounded projections such that the Banach algebra of ope

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11

WEI, GUI-WU. "UNCERTAIN LINGUISTIC HYBRID GEOMETRIC MEAN OPERATOR AND ITS APPLICATION TO GROUP DECISION MAKING UNDER UNCERTAIN LINGUISTIC ENVIRONMENT." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, no. 02 (2009): 251–67. http://dx.doi.org/10.1142/s021848850900584x.

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In this paper, we propose an uncertain linguistic hybrid geometric mean (ULHGM) operator, which is based on the uncertain linguistic weighted geometric mean (ULWGM) operator and the uncertain linguistic ordered weighted geometric (ULOWG) operator proposed by Xu [Z. S. Xu, "An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations", Decision Support Systems41 (2006) 488–499] and study some desirable properties of the ULHGM operator. We have proved both ULWGM and ULOWG operators are the spec

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12

Chen, Liuhao, Zeshui Xu, and Xiaohan Yu. "The ordered multiplicative modular geometric operator." Knowledge-Based Systems 39 (February 2013): 144–50. http://dx.doi.org/10.1016/j.knosys.2012.10.014.

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13

Zhou, Ligang, Yingdong He, Huayou Chen, and Jinpei Liu. "On Compatibility of Interval Multiplicative Preference Relations Based on the COWGA Operator." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 22, no. 03 (2014): 407–28. http://dx.doi.org/10.1142/s0218488514500202.

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The aim of this paper is to develop a new compatibility, which is very suitable to deal with group decision making (GDM) problems involving interval multiplicative preference relations, based on the continuous ordered weighted geometric averaging (COWGA) operator. First, we define some concepts of the compatibility degree and the compatibility index for the two interval multiplicative preference relations based on the COWGA operator. Then, we study some desirable properties of the compatibility index and investigate the relationship between each expert's interval multiplicative preference rela

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14

Aydın, Abdullah, and Svetlana Gorokhova. "Multiplicative order compact operators between vector lattices and Riesz algebras." Filomat 38, no. 19 (2024): 6743–51. https://doi.org/10.2298/fil2419743a.

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In this paper, we present and examine the concept of multiplicative order compact operators from vector lattices to Riesz algebras. Specifically, a linear operator T from a vector lattice X to an Riesz algebra E is deemed omo-compact, if every net x? in an o-bounded subset of X possesses a subnet x?? such that Tx??mo--? y for some y ? E. Moreover, we introduce and investigate omo-M-and omo-L-weakly compact operators.

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15

Drnovšek, Roman. "Triangularizing semigroups of positive operators on an atomic normed Riesz Space." Proceedings of the Edinburgh Mathematical Society 43, no. 1 (2000): 43–55. http://dx.doi.org/10.1017/s001309150002068x.

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AbstractIn the first part of the paper we prove several results on the existence of invariant closed ideals for semigroups of bounded operators on a normed Riesz space (of dimension greater than 1) possessing an atom. For instance, if S is a multiplicative semigroup of positive operators on such space that are locally quasinilpotent at the same atom, then S has a non-trivial invariant closed ideal. Furthermore, if T is a non-zero positive operator that is quasinilpotent at an atom and if S is a multiplicative semigroup of positive operators such that TS ≤ ST for all S ∈ S, then S and T have a

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16

Zhang, Sheng, Sen Zhao, and Yue Zhang. "Extending operator method to local fractional evolution equations in fluids." Thermal Science 23, no. 6 Part B (2019): 3759–66. http://dx.doi.org/10.2298/tsci180820261z.

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This paper is aimed to solve non-linear local fractional evolution equations in fluids by extending the operator method proposed by Zenonas Navickas. Firstly, we give the definitions of the generalized operator of local fractional differentiation and the multiplicative local fractional operator. Secondly, some properties of the defined operators are proved. Thirdly, a solution in the form of operator representation of a local fractional ordinary differential equation is obtained by the extended operator method. Finally, with the help of the obtained solution in the form of operator representat

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17

GONZÁLEZ-TOKMAN, CECILIA, and ANTHONY QUAS. "A semi-invertible operator Oseledets theorem." Ergodic Theory and Dynamical Systems 34, no. 4 (2013): 1230–72. http://dx.doi.org/10.1017/etds.2012.189.

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AbstractSemi-invertible multiplicative ergodic theorems establish the existence of an Oseledets splitting for cocycles of non-invertible linear operators (such as transfer operators) over an invertible base. Using a constructive approach, we establish a semi-invertible multiplicative ergodic theorem that for the first time can be applied to the study of transfer operators associated to the composition of piecewise expanding interval maps randomly chosen from a set of cardinality of the continuum. We also give an application of the theorem to random compositions of perturbations of an expanding

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18

Dragomir, Silvestru Sever. "Some Multiplicative Inequalities for Heinz Operator Mean." Mathematical Analysis and Convex Optimization 2, no. 1 (2021): 1–10. http://dx.doi.org/10.52547/maco.2.1.1.

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19

OLIVIER, D., and G. VALENT. "MULTIPLICATIVE RENORMALIZABILITY AND THE LAPLACE-BELTRAMI OPERATOR." International Journal of Modern Physics A 06, no. 06 (1991): 955–76. http://dx.doi.org/10.1142/s0217751x91000526.

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For some rank 1 non-linear σ models we prove that a necessary and sufficient condition of multiplicative renormalizability for composite fields is that they should be eigenfunctions of the coset Laplace-Beltrami operator. These eigenfunctions span the irreducible representation space of the isometry group and may be finite- or infinite-dimensional. The zero mode of the Laplace-Beltrami operator plays a particular role since it is not renormalized at all.

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20

Früchtl, Felix. "Multiplicative operator functions and abstract Cauchy problems." Banach Journal of Mathematical Analysis 12, no. 2 (2018): 347–73. http://dx.doi.org/10.1215/17358787-2017-0042.

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21

Liu, Fuxiang, та Jielan Li. "Analytical Properties and Hermite–Hadamard Type Inequalities Derived from Multiplicative Generalized Proportional σ-Riemann–Liouville Fractional Integrals". Symmetry 17, № 5 (2025): 702. https://doi.org/10.3390/sym17050702.

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This paper investigates the analytical properties of multiplicative generalized proportional σ-Riemann–Liouville fractional integrals and the corresponding Hermite–Hadamard-type inequalities. Central to our study are two key notions: multiplicative σ-convex functions and multiplicative generalized proportional σ-Riemann–Liouville fractional integrals, both of which serve as the foundational framework for our analysis. We first introduce and examine several fundamental properties of the newly defined fractional integral operator, including continuity, commutativity, semigroup behavior, and boun

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22

Li, Fang, Jin Liang, Ti-Jun Xiao, and Jun Zhang. "On Perturbation of ConvolutedC-Regularized Operator Families." Journal of Function Spaces and Applications 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/579326.

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Of concern are two classes of convolutedC-regularized operator families: convolutedC-cosine operator families and convolutedC-semigroups. We obtain new and general multiplicative and additive perturbation theorems for these convolutedC-regularized operator families. Two examples are given to illustrate our abstract results.

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23

Xu, Chuan Yu, and Zhen Ming Ma. "Symmetric intuitionistic multiplicative aggregation operator for group decision making in intuitionistic multiplicative environments." Journal of Intelligent & Fuzzy Systems 36, no. 6 (2019): 5909–18. http://dx.doi.org/10.3233/jifs-181735.

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24

Wu, Qiongling, Jian Lin, Shaohan Zhang, and Zhiyong Tian. "A Theil coefficient-based combination prediction method with interval heterogeneous information for wind energy prediction." Journal of Intelligent & Fuzzy Systems 41, no. 1 (2021): 1031–48. http://dx.doi.org/10.3233/jifs-210004.

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This paper constructs the continuous-Young optimal weighted arithmetic averaging (C-YOWA) operator and the continuous-Young optimal weighted geometric (C-YOWG) operator based on definite integral and Young inequality. A series of special cases and main properties of the proposed aggregation operators are also investigated. In order to integrate heterogeneous interval data and obtain more accurate prediction results, the heterogeneous interval combination prediction (HICP) model based on C-YOWA operator, C-YOWG operator and Theil coefficient is proposed. The HICP model consider not only the exi

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25

Vassilev, Peter, and Vassia Atanassova. "On a new expanding modal-like operator on intuitionistic fuzzy sets." Notes on Intuitionistic Fuzzy Sets 30, no. 4 (2024): 368–73. https://doi.org/10.7546/nifs.2024.30.4.368-373.

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26

Alam, Noor, Waseem Ahmad Khan, Can Kızılateş, and Cheon Seoung Ryoo. "Two-Variable q-General-Appell Polynomials Within the Context of the Monomiality Principle." Mathematics 13, no. 5 (2025): 765. https://doi.org/10.3390/math13050765.

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In this study, we consider the two-variable q-general polynomials and derive some properties. By using these polynomials, we introduce and study the theory of two-variable q-general Appell polynomials (2VqgAP) using q-operators. The effective use of the q-multiplicative operator of the base polynomial produces the generating equation for 2VqgAP involving the q-exponential function. Furthermore, we establish the q-multiplicative and q-derivative operators and the corresponding differential equations. Then, we obtain the operational, explicit and determinant representations for these polynomials

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27

Ricker, W. "Countable additivity of multiplicative operator-valued set functions." Acta Mathematica Hungarica 47, no. 1-2 (1986): 121–26. http://dx.doi.org/10.1007/bf01949132.

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28

Thaheem, A. B., and AbdulRahim Khan. "On some properties of Banach operators." International Journal of Mathematics and Mathematical Sciences 27, no. 3 (2001): 149–53. http://dx.doi.org/10.1155/s0161171201006251.

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A mappingαfrom a normed spaceXinto itself is called a Banach operator if there is a constantksuch that0≤k<1and‖α2(x)−α(x)‖≤k‖α(x)−x‖for allx∈X. In this note we study some properties of Banach operators. Among other results we show that ifαis a linear Banach operator on a normed spaceX, thenN(α−1)=N((α−1)2),N(α−1)∩R(α−1)=(0)and ifXis finite dimensional thenX=N(α−1)⊕R(α−1), whereN(α−1)andR(α−1)denote the null space and the range space of(α−1), respectively and 1 is the identity mapping onX. We also obtain some commutativity results for a pair of bounded linear multiplicative Banach operators

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29

Kadak, Ugur. "On multiplicative difference sequence spaces and related dual properties." Boletim da Sociedade Paranaense de Matemática 35, no. 3 (2017): 181–93. http://dx.doi.org/10.5269/bspm.v35i3.29182.

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The main purpose of the present article is to introduce the multiplicative difference sequence spaces of order $m$ by defining the multiplicative difference operator $\Delta_{*}^m(x_k)=x^{}_k~x^{-m}_{k+1}~x^{\binom{m}{2}}_{k+2}~x^{-\binom{m}{3}}_{k+3}~x^{\binom{m}{4}}_{k+4}\dots x^{(-1)^m}_{k+m}$ for all $m, k \in \mathbb N$. By using the concept of multiplicative linearity various topological properties are investigated and the relations related to their dual spaces are studied via multiplicative infinite matrices.

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30

Ferreira, João Carlos da Motta, та Maria das Graças Bruno Marietto. "Multiplicative Jordan triple (θ,ϕ) -derivations of rings and standard operator algebras". Algebra and Discrete Mathematics 39, № 1 (2025): 89–96. https://doi.org/10.12958/adm2313.

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31

Bytsenko, A. A., E. Elizalde, and M. E. X. Guimarães. "Operator Product on Locally Symmetric Spaces of Rank One and the Multiplicative Anomaly." International Journal of Modern Physics A 18, no. 12 (2003): 2179–87. http://dx.doi.org/10.1142/s0217751x03015635.

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The global multiplicative properties of Laplace type operators acting on irreducible rank one symmetric spaces are considered. The explicit form of the multiplicative anomaly is derived and its corresponding value is calculated exactly, for important classes of locally symmetric spaces and different dimensions.

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32

Nagolkina, Zoya, and Yuri Filonov. "SCHEME OF MULTIPLICATIVE REPRESENTATIONS FOR A STOCHASTIC EQUATION WITH TWO WIENER PROCESSES." APPLIED GEOMETRY AND ENGINEERING GRAPHICS, no. 102 (June 27, 2022): 136–48. http://dx.doi.org/10.32347/0131-579x.2022.102.136-148.

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In this paper we consider a stochastic differential equation with two independent Wiener processes in an infinite-dimensional Hilbert space. This equation can be a mathematical model of a dynamic system in the presence of several independent perturbing random factors. To study the parameters of this equation, the Daletsky-Trotter method of multiplicative representations is used. This method is applied to both deterministic and stochastic equations. The method consists in the following: one constructs a partition of the interval of existence of the solution [t0, T] into elementary [tk+1, tk]. O

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33

Marrero, Isabel. "On the Symbols of Strictly m-Null Elementary Operators." Mathematics 13, no. 12 (2025): 2026. https://doi.org/10.3390/math13122026.

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This paper extends the previous work by the author on m-null pairs of operators in Hilbert space. If an elementary operator L has elementary symbols A and B that are p-null and q-null, respectively, then L is (p+q−1)-null. Here, we prove the converse under strictness conditions, modulo some nonzero multiplicative constant—if L is strictly (p+q−1)-null, then a scalar λ≠0 exists such that λA is strictly p-null and λ−1B is strictly q-null. Our constructive argument relies essentially on algebraic and combinatorial methods. Thus, the result obtained by Gu on m-isometries is recovered without resor

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34

Lin, Jian, Riqing Chen, and Qiang Zhang. "Similarity-Based Approach for Group Decision Making with Multi-Granularity Linguistic Information." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 24, no. 06 (2016): 873–900. http://dx.doi.org/10.1142/s0218488516500409.

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The aim of this article is to investigate the approach for multi-attribute group decision-making, in which the attribute values take the form of multi-granularity multiplicative linguistic information. Firstly, to process multiple sources of decision information assessed in different multiplicative linguistic label sets, a method for transforming multi-granularity multiplicative linguistic information into multiplicative trapezoidal fuzzy numbers is proposed. Then, a formula for ranking multiplicative trapezoidal fuzzy numbers is given based on geometric mean. Furthermore, the concept of simil

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35

Ferreira, João Carlos, and Maria das Graças Bruno Marietto. "Multiplicative Jordan triple semi-derivations on rings and standard operator algebras." Annals of Mathematics and Computer Science 20 (January 3, 2024): 98–106. http://dx.doi.org/10.56947/amcs.v20.234.

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36

Ferreira, João Carlos da Motta, and Maria das Graças Bruno Marietto. "Additivity of multiplicative Jordan higher semi-derivations on rings and standard operator algebras." Annals of Mathematics and Computer Science 26 (January 5, 2025): 92–104. https://doi.org/10.56947/amcs.v26.448.

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37

Kribs, David W., Jeremy Livick, Mike I. Nelson, Rajesh Perira, and Mizanur Rahaman. "Quantum complementarity and operator structures." Quantum Information and Computation 19, no. 1&2 (2019): 67–83. http://dx.doi.org/10.26421/qic19.1-2-5.

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We establish operator structure identities for quantum channels and their error-correcting and private codes, emphasizing the complementarity relationship between the two perspectives. Relevant structures include correctable and private operator algebras, and operator spaces such as multiplicative domains and nullspaces of quantum channels and their complementary maps. For the case of privatizing to quantum states, we also derive dimension inequalities on the associated operator algebras that further quantify the trade-off between correction and privacy.

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Ferreira, João Carlos, and Maria das Graças Bruno Marietto. "Multiplicative Jordan triple higher semi-derivations on rings and standard operator algebras." Annals of Mathematics and Computer Science 22 (March 28, 2024): 54–61. http://dx.doi.org/10.56947/amcs.v22.270.

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39

Ashraf, Mohammad, Bilal Ahmad Wani, and Feng Wei. "Multiplicative ∗-lie triple higher derivations of standard operator algebras." Quaestiones Mathematicae 42, no. 7 (2018): 857–84. http://dx.doi.org/10.2989/16073606.2018.1502213.

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40

Wani, Bilal Ahmad, Mohammad Ashraf, and Mohd Shuaib Akhtar. "Multiplicative *-Lie type higher derivations of standard operator algebras." Communications in Algebra 49, no. 9 (2021): 3777–97. http://dx.doi.org/10.1080/00927872.2021.1906266.

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41

An, Runling, and Jinchuan Hou. "ADDITIVITY OF JORDAN MULTIPLICATIVE MAPS ON JORDAN OPERATOR ALGEBRAS." Taiwanese Journal of Mathematics 10, no. 1 (2006): 45–64. http://dx.doi.org/10.11650/twjm/1500403798.

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42

Dong, Aiju, Linzhe Huang, and Boqing Xue. "Operator algebras associated with multiplicative convolutions of arithmetic functions." Science China Mathematics 61, no. 9 (2018): 1665–76. http://dx.doi.org/10.1007/s11425-017-9281-0.

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43

Klein, Christoph, and Robert Strzodka. "Preconditioning Sparse Matrices with Alternating and Multiplicative Operator Splittings." SIAM Journal on Scientific Computing 45, no. 1 (2023): A25—A48. http://dx.doi.org/10.1137/21m1430492.

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44

Weiß, Christian H., and Fukang Zhu. "Conditional-mean multiplicative operator models for count time series." Computational Statistics & Data Analysis 191 (March 2024): 107885. http://dx.doi.org/10.1016/j.csda.2023.107885.

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45

Horne, Ross. "The Consistency and Complexity of Multiplicative Additive System Virtual." Scientific Annals of Computer Science XXV, no. 2 (2015): 245–316. https://doi.org/10.7561/SACS.2015.2.245.

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This paper investigates the proof theory of multiplicative additive system virtual (MAV). MAV combines two established proof calculi: multiplicative additive linear logic (MALL) and basic system virtual (BV). Due to the presence of the self-dual non-commutative operator from BV, the calculus MAV is defined in the calculus of structures – a generalisation of the sequent calculus where inference rules can be applied in any context. A generalised cut elimination result is proven for MAV, thereby establishing the consistency of linear implication defined in the calculus. The cut elimination

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46

Enock, Michel. "QUANTUM GROUPOIDS OF COMPACT TYPE." Journal of the Institute of Mathematics of Jussieu 4, no. 1 (2005): 29–133. http://dx.doi.org/10.1017/s1474748005000022.

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To any groupoid, equipped with a Haar system, Jean-Michel Vallin had associated several objects (pseudo-multiplicative unitary, Hopf-bimodule) in order to generalize, up to the groupoid case, the classical notions of multiplicative unitary and Hopf–von Neumann algebra, which were intensely used to construct quantum groups in the operator algebra setting. In two former articles (one in collaboration with Jean-Michel Vallin), starting from a depth-2 inclusion of von Neumann algebras, we have constructed such objects, which allowed us to study two ‘quantum groupoids’ dual to each other. We are no

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Hervé, Loïc, Sana Louhichi, and Françoise Pène. "Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains." ESAIM: Probability and Statistics 23 (2019): 607–37. http://dx.doi.org/10.1051/ps/2019003.

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This article is motivated by the quantitative study of the exponential growth of Markov-driven bifurcating processes [see Hervé et al., ESAIM: PS 23 (2019) 584–606]. In this respect, a key property is the multiplicative ergodicity, which deals with the asymptotic behaviour of some Laplace-type transform of nonnegative additive functional of a Markov chain. We establish a spectral version of this multiplicative ergodicity property in a general framework. Our approach is based on the use of the operator perturbation method. We apply our general results to two examples of Markov chains, including

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Nagolkina, Zoya, and Yuri Filonov. "MULTIPLICATIVE APPROXIMATION OF A RANDOM PROCESS." APPLIED GEOMETRY AND ENGINEERING GRAPHICS, no. 100 (May 24, 2021): 205–14. http://dx.doi.org/10.32347/0131-579x.2021.100.205-214.

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In this paper we consider the stochastic Ito differential equation in an infinite-dimensional real Hilbert space. Using the method of multiplicative representations of Daletsky - Trotter, its approximate solution is constructed. Under classical conditions on the coefficients, there is a single to the stochastic equivalence of solutions of the stochastic equation, which is a random process. This development generates an evolutionary family of resolving operators by the formula x(t)= S(t, Construct the division of the segment by the points. An equation with time-uniform coefficients is con

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49

Longstaff, W. E., and H. Radjavi. "On Permutability and Submultiplicativity of Spectral Radius." Canadian Journal of Mathematics 47, no. 5 (1995): 1007–22. http://dx.doi.org/10.4153/cjm-1995-053-x.

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AbstractLet r(T) denote the spectral radius of the operator T acting on a complex Hilbert space H. Let S be a multiplicative semigroup of operators on H. We say that r is permutable on 𝓢 if r(ABC) = r(BAC), for every A,B,C ∈ 𝓢. We say that r is submultiplicative on 𝓢 if r(AB) ≤ r(A)r(B), for every A, B ∈ 𝓢. It is known that, if r is permutable on 𝓢, then it is submultiplicative. We show that the converse holds in each of the following cases: (i) 𝓢 consists of compact operators (ii) 𝓢 consists of normal operators (iii) 𝓢 is generated by orthogonal projections.

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50

Furuichi, Shigeru, and Hamid Reza Moradi. "On further refinements for Young inequalities." Open Mathematics 16, no. 1 (2018): 1478–82. http://dx.doi.org/10.1515/math-2018-0115.

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AbstractIn this paper sharp results on operator Young’s inequality are obtained. We first obtain sharp multiplicative refinements and reverses for the operator Young’s inequality. Secondly, we give an additive result, which improves a well-known inequality due to Tominaga. We also provide some estimates for the difference A1/2(A−1/2BA−1/2)vA1/2-{(1-v)A + vB} for v∉[ 0,1].

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