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Journal articles on the topic 'Block operator matrices'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

Albeverio, Sergio, Konstantin A. Makarov, and Alexander K. Motovilov. "Graph Subspaces and the Spectral Shift Function." Canadian Journal of Mathematics 55, no. 3 (2003): 449–503. http://dx.doi.org/10.4153/cjm-2003-020-7.

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AbstractWe obtain a new representation for the solution to the operator Sylvester equation in the form of a Stieltjes operator integral. We also formulate new sufficient conditions for the strong solvability of the operator Riccati equation that ensures the existence of reducing graph subspaces for block operator matrices. Next, we extend the concept of the Lifshits-Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of admissible operators that are similar to self-adjoint operators. Based on this new concept we express the spectral shift functio

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2

Abdelmoumen, Boulbeba, and Sonia Yengui. "Perturbation theory, M-essential spectra of operator matrices." Filomat 34, no. 4 (2020): 1187–96. http://dx.doi.org/10.2298/fil2004187a.

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In this paper, we will establish some results on perturbation theory of block operator matrices acting on Xn, where X is a Banach space. These results are exploited to investigate the M-essential spectra of a general class of operators defined by a 3x3 block operator matrix acting on a product of Banach spaces X3.

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3

Abdelmoumen, Boulbeba, and Sonia Yengui. "Perturbation theory, M-essential spectra of operator matrices." Filomat 34, no. 4 (2020): 1187–96. http://dx.doi.org/10.2298/fil2004187a.

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In this paper, we will establish some results on perturbation theory of block operator matrices acting on Xn, where X is a Banach space. These results are exploited to investigate the M-essential spectra of a general class of operators defined by a 3x3 block operator matrix acting on a product of Banach spaces X3.

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4

Liu, Rufang, Haiyan Zhang, and Chunyuan Deng. "On the mixed-type generalized inverses of the products of two operators." Filomat 33, no. 14 (2019): 4361–76. http://dx.doi.org/10.2298/fil1914361l.

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Let A, B and be closed range operators. The explicit matrix expressions for various generalized inverses are obtained by using block operator matrix methods. Some subtle relationships between the properties of sub-blocks in operator matrices A, B and their range relations are built. New necessary and sufficient conditions for the equivalent relations, inclusion relations and mixed-type generalized inverses relations are presented. Some recent mixed-type reverse-order laws results are covered and many new mixed-type generalized inverses relations are established by using this block-operator mat

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5

Rasulov, Tulkin Khusenovich, and Zarina Erkin kizi Mustafoeva. "ON THE POIN ON THE POINT SPECTRUM OF OPERA TRUM OF OPERATOR MATRIX COMIMG T X COMIMG TO A A DIAGONALIZABLE MATRIX." Scientific Reports of Bukhara State University 3, no. 4 (2019): 14–19. http://dx.doi.org/10.52297/2181-1466/2019/3/4/4.

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It isconsidered herethediagonalizable operatormatrix . The essential and point spectrum of are described via the spectrum of the more simpler operator matrices. If the elements of a matrix are linear operators in Banach or Hilbert spaces, then it is called a block-operator matrix. One of the special classes of block operator matrices are the Hamiltonians of a system with a nonconserved number of quantum particles on an integer or noninteger lattice. The inclusion for the discrete spectrum of is established.

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6

Filipiak, Katarzyna, Daniel Klein, and Erika Vojtková. "The properties of partial trace and block trace operators of partitioned matrices." Electronic Journal of Linear Algebra 33 (May 16, 2018): 3–15. http://dx.doi.org/10.13001/1081-3810.3688.

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The aim of this paper is to give the properties of two linear operators defined on non-square partitioned matrix: the partial trace operator and the block trace operator. The conditions for symmetry, nonnegativity, and positive-definiteness are given, as well as the relations between partial trace and block trace operators with standard trace, vectorizing and the Kronecker product operators. Both partial trace as well as block trace operators can be widely used in statistics, for example in the estimation of unknown parameters under the multi-level multivariate models or in the theory of exper

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7

Yu, Jiahui, Alatancang Chen, Junjie Huang, and Jiaojiao Wu. "Approximation of the block numerical range of block operator matrices." Filomat 33, no. 12 (2019): 3877–81. http://dx.doi.org/10.2298/fil1912877y.

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8

Jiang, Xiaoyu, and Kicheon Hong. "Equalities and Inequalities for Norms of Block Imaginary Circulant Operator Matrices." Abstract and Applied Analysis 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/521214.

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Circulant, block circulant-type matrices and operator norms have become effective tools in solving networked systems. In this paper, the block imaginary circulant operator matrices are discussed. By utilizing the special structure of such matrices, several norm equalities and inequalities are presented. The normτin consideration is the weakly unitarily invariant norm, which satisfiesτA=τ(UAV). The usual operator norm and Schattenp-norm are included. Furthermore, some special cases and examples are given.

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9

Tretter, Christiane. "Spectral inclusion for unbounded block operator matrices." Journal of Functional Analysis 256, no. 11 (2009): 3806–29. http://dx.doi.org/10.1016/j.jfa.2008.12.024.

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10

BOURIN, JEAN-CHRISTOPHE. "MATRIX SUBADDITIVITY INEQUALITIES AND BLOCK-MATRICES." International Journal of Mathematics 20, no. 06 (2009): 679–91. http://dx.doi.org/10.1142/s0129167x09005509.

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We give a number of subadditivity results and conjectures for symmetric norms, matrices and block-matrices. Let A, B, Z be matrices of same size and suppose that A, B are normal and Z is expansive, i.e. Z*Z ≥ I. We conjecture that [Formula: see text] for all non-negative concave function f on [0,∞) and all symmetric norms ‖ · ‖ (in particular for all Schatten p-norms). This would extend known results for positive operator to all normal operators. We prove these inequalities in several cases and we propose some related open questions, both in the positive and normal cases. As nice applications

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11

Caswell, Hal, and Silke F. van Daalen. "A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices." Journal of Applied Mathematics 2016 (2016): 1–3. http://dx.doi.org/10.1155/2016/4590817.

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The vec operator transforms a matrix to a column vector by stacking each column on top of the next. It is useful to write the vec of a block-structured matrix in terms of the vec operator applied to each of its component blocks. We derive a simple formula for doing so, which applies regardless of whether the blocks are of the same or of different sizes.

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12

Jeribi, Aref, Nedra Moalla, and Ines Walha. "Spectra of some block operator matrices and application to transport operators." Journal of Mathematical Analysis and Applications 351, no. 1 (2009): 315–25. http://dx.doi.org/10.1016/j.jmaa.2008.09.074.

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13

Langer, H., M. Langer, and Christiane Tretter. "Variational principles for eigenvalues of block operator matrices." Indiana University Mathematics Journal 51, no. 6 (2002): 1427–60. http://dx.doi.org/10.1512/iumj.2002.51.2286.

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14

Kostenko, Aleksey. "A Note on J-positive Block Operator Matrices." Integral Equations and Operator Theory 81, no. 1 (2014): 113–25. http://dx.doi.org/10.1007/s00020-014-2156-7.

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15

Arlinskiĭ, Yury. "The Schur Problem and Block Operator CMV Matrices." Complex Analysis and Operator Theory 8, no. 4 (2013): 875–923. http://dx.doi.org/10.1007/s11785-013-0317-3.

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16

Deng, Chunyuan. "On the group invertibility of operators." Electronic Journal of Linear Algebra 31 (February 5, 2016): 492–510. http://dx.doi.org/10.13001/1081-3810.1967.

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The main topic of this paper is the group invertibility of operators in Hilbert spaces. Conditions for the existence of the group inverses of products of two operators and the group invertibility of anti-triangular block operator matrices are studied. The equivalent conditions related to the reverse order law for the group inverses of operators are obtained.

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17

Chryssomalakos, Chryssomalis, and Christopher R. Stephens. "Covariant Genetic Dynamics." Evolutionary Computation 15, no. 3 (2007): 291–320. http://dx.doi.org/10.1162/evco.2007.15.3.291.

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We present a covariant form for the dynamics of a canonical GA of arbitrary cardinality, showing how each genetic operator can be uniquely represented by a mathematical object — a tensor — that transforms simply under a general linear coordinate transformation. For mutation and recombination these tensors can be written as tensor products of the analogous tensors for one-bit strings thus giving a greatly simplified formulation of the dynamics. We analyze the three most well known coordinate systems — string, Walsh and Building Block — discussing their relative advantages and disadvantages with

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18

Ploymukda, Arnon, and Pattrawut Chansangiam. "Norm estimations, continuity, and compactness for Khatri-Rao products of Hilbert Space operators." Malaysian Journal of Fundamental and Applied Sciences 14, no. 4 (2018): 382–86. http://dx.doi.org/10.11113/mjfas.v14n4.881.

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We provide estimations for the operator norm, the trace norm, and the Hilbert-Schmidt norm for Khatri-Rao products of Hilbert space operators. It follows that the Khatri-Rao product is continuous on norm ideals of compact operators equipped with the topologies induced by such norms. Moreover, if two operators are represented by block matrices in which each block is nonzero, then their Khatri-Rao product is compact if and only if both operators are compact. The Khatri-Rao product of two operators are trace-class (Hilbert-Schmidt class) if and only if each factor is trace-class (Hilbert-Schmidt

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19

Zou, Honglin, Dijana Mosić, and Jianlong Chen. "The existence and representation of the Drazin inverse of a 2 × 2 block matrix over a ring." Journal of Algebra and Its Applications 18, no. 11 (2019): 1950212. http://dx.doi.org/10.1142/s0219498819502128.

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In this paper, further results on the Drazin inverse are obtained in a ring. Several representations of the Drazin inverse of [Formula: see text] block matrices over an arbitrary ring are given under new conditions. Also, upper bounds for the Drazin index of block matrices are studied. Numerical examples are given to illustrate our results. Necessary and sufficient conditions for the existence as well as the expression of the group inverse of block matrices are obtained under certain conditions. In particular, some results of related papers which were considered for complex matrices, operator

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20

HUANG, JunJie, YaRu QI, and atancang Al. "Spectral inclusion properties of some unbounded block operator matrices." SCIENTIA SINICA Mathematica 44, no. 10 (2014): 1099–110. http://dx.doi.org/10.1360/n012013-00104.

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21

Albeverio, Sergio, and Alexei Konstantinov. "On the absolutely continuous spectrum of block operator matrices." Mathematische Nachrichten 281, no. 8 (2008): 1079–87. http://dx.doi.org/10.1002/mana.200510661.

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22

Konstantinov, Alexei, and Reinhard Mennicken. "On the Friedrichs extension of some block operator matrices." Integral Equations and Operator Theory 42, no. 4 (2002): 472–81. http://dx.doi.org/10.1007/bf01270924.

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23

Giribet, Juan, Matthias Langer, Francisco Martínez Pería, Friedrich Philipp, and Carsten Trunk. "Spectral enclosures for a class of block operator matrices." Journal of Functional Analysis 278, no. 10 (2020): 108455. http://dx.doi.org/10.1016/j.jfa.2019.108455.

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24

Adamjan, Vadim, and Heinz Langer. "The Spectral Shift Function for Certain Block Operator Matrices." Mathematische Nachrichten 211, no. 1 (2000): 5–24. http://dx.doi.org/10.1002/(sici)1522-2616(200003)211:1<5::aid-mana5>3.0.co;2-u.

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25

Bögli, Sabine, and Marco Marletta. "Essential numerical ranges for linear operator pencils." IMA Journal of Numerical Analysis 40, no. 4 (2019): 2256–308. http://dx.doi.org/10.1093/imanum/drz049.

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Abstract We introduce concepts of essential numerical range for the linear operator pencil $\lambda \mapsto A-\lambda B$. In contrast to the operator essential numerical range, the pencil essential numerical ranges are, in general, neither convex nor even connected. The new concepts allow us to describe the set of spectral pollution when approximating the operator pencil by projection and truncation methods. Moreover, by transforming the operator eigenvalue problem $Tx=\lambda x$ into the pencil problem $BTx=\lambda Bx$ for suitable choices of $B$, we can obtain nonconvex spectral enclosures f

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26

Nikabadze, Mikhail, and Armine Ulukhanyan. "Some Applications of Eigenvalue Problems for Tensor and Tensor–Block Matrices for Mathematical Modeling of Micropolar Thin Bodies." Mathematical and Computational Applications 24, no. 1 (2019): 33. http://dx.doi.org/10.3390/mca24010033.

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The statement of the eigenvalue problem for a tensor–block matrix (TBM) of any orderand of any even rank is formulated, and also some of its special cases are considered. In particular,using the canonical presentation of the TBM of the tensor of elastic modules of the micropolartheory, in the canonical form the specific deformation energy and the constitutive relations arewritten. With the help of the introduced TBM operator, the equations of motion of a micropolararbitrarily anisotropic medium are written, and also the boundary conditions are written down bymeans of the introduced TBM operato

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27

Niezgoda, Marek. "A note on majorization properties of the Lieb function." Electronic Journal of Linear Algebra 36, no. 36 (2020): 134–42. http://dx.doi.org/10.13001/ela.2020.5043.

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In this note, the Lieb function $(A,B) \to \Phi (A,B) = \tr \exp ( A + \log B )$ for an Hermitian matrix $A$ and a positive definite matrix $B$ is studied. It is shown that $\Phi$ satisfies a majorization property of Sherman type induced by a doubly stochastic operator. The variant for commuting matrices is also considered. An interpretation is given for the case of the orthoprojection operator onto the space of block diagonal matrices.

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28

Langer, Matthias, and Michael Strauss. "Spectral properties of unbounded $J$-self-adjoint block operator matrices." Journal of Spectral Theory 7, no. 1 (2017): 137–90. http://dx.doi.org/10.4171/jst/158.

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29

IPEK AL, PEMBE, and Zameddin ISMAILOV. "Schatten-von Neumann characteristic of infinite tridiagonal block operator matrices." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 68, no. 2 (2019): 1852–66. http://dx.doi.org/10.31801/cfsuasmas.474512.

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30

Charfi, Salma, and Ines Walha. "ON RELATIVE ESSENTIAL SPECTRA OF BLOCK OPERATOR MATRICES AND APPLICATION." Bulletin of the Korean Mathematical Society 53, no. 3 (2016): 681–98. http://dx.doi.org/10.4134/bkms.b150233.

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31

Adamyan, Vadim, Heinz Langer, Reinhard Mennicken, and Josef Saurer. "Spectral Components of Selfadjoint Block Operator Matrices with Unbounded Entries." Mathematische Nachrichten 178, no. 1 (1996): 43–80. http://dx.doi.org/10.1002/mana.19961780103.

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32

Aghideh, M. Ghaderi, M. S. Moslehian, and J. Rooin. "Sharp Inequalities for the Numerical Radii of Block Operator Matrices." Analysis Mathematica 45, no. 4 (2019): 687–703. http://dx.doi.org/10.1007/s10476-019-0002-5.

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33

Muhammad, Ahmed, and Marco Marletta. "Approximation of the Quadratic Numerical Range of Block Operator Matrices." Integral Equations and Operator Theory 74, no. 2 (2012): 151–62. http://dx.doi.org/10.1007/s00020-012-1971-y.

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34

Trostorff, Sascha. "On a Class of Block Operator Matrices in System Theory." Complex Analysis and Operator Theory 11, no. 4 (2016): 947–60. http://dx.doi.org/10.1007/s11785-016-0556-1.

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35

Radl, Agnes, and Manfred P. H. Wolff. "Topological properties of the block numerical range of operator matrices." Operators and Matrices, no. 4 (2020): 1001–14. http://dx.doi.org/10.7153/oam-2020-14-62.

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36

Tarcsay, Zsigmond, and Tamás Titkos. "Operators on Anti-dual pairs: Self-adjoint Extensions and the Strong Parrott Theorem." Canadian Mathematical Bulletin 63, no. 4 (2020): 813–24. http://dx.doi.org/10.4153/s0008439520000065.

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AbstractThe aim of this paper is to develop an approach to obtain self-adjoint extensions of symmetric operators acting on anti-dual pairs. The main advantage of such a result is that it can be applied for structures not carrying a Hilbert space structure or a normable topology. In fact, we will show how hermitian extensions of linear functionals of involutive algebras can be governed by means of their induced operators. As an operator theoretic application, we provide a direct generalization of Parrott’s theorem on contractive completion of 2 by 2 block operator-valued matrices. To exhibit th

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37

Xu, Qingxiang, Chuanning Song, and Lili He. "Representations for the group inverse of anti-triangular block operator matrices." Linear Algebra and its Applications 443 (February 2014): 191–203. http://dx.doi.org/10.1016/j.laa.2013.11.018.

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38

Moslehian, Mohammad Sal, and Mostafa Sattari. "Inequalities for operator space numerical radius of 2 × 2 block matrices." Journal of Mathematical Physics 57, no. 1 (2016): 015201. http://dx.doi.org/10.1063/1.4926977.

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39

Förster, K. H., and M. M. Nafalska. "A factorization of extremal extensions with applications to block operator matrices." Acta Mathematica Hungarica 129, no. 1-2 (2010): 112–41. http://dx.doi.org/10.1007/s10474-010-9248-x.

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40

Strauss, Michael. "Spectral Estimates and Basis Properties for Self-Adjoint Block Operator Matrices." Integral Equations and Operator Theory 67, no. 2 (2010): 257–77. http://dx.doi.org/10.1007/s00020-010-1780-0.

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41

Wojtylak, Michał. "Noncommuting Domination in Krein Spaces Via Commutators of Block Operator Matrices." Integral Equations and Operator Theory 59, no. 1 (2007): 129–47. http://dx.doi.org/10.1007/s00020-007-1506-0.

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42

Arlinskiĭ, Yury M., Seppo Hassi, and Henk S. V. de Snoo. "Parametrization of Contractive Block Operator Matrices and Passive Discrete-Time Systems." Complex Analysis and Operator Theory 1, no. 2 (2007): 211–33. http://dx.doi.org/10.1007/s11785-007-0014-1.

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43

Axelsson, Owe, and János Karátson. "Krylov improvements of the Uzawa method for Stokes type operator matrices." Numerische Mathematik 148, no. 3 (2021): 611–31. http://dx.doi.org/10.1007/s00211-021-01208-5.

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AbstractThe paper is devoted to Krylov type modifications of the Uzawa method on the operator level for the Stokes problem in order to accelerate convergence. First block preconditioners and their effect on convergence are studied. Then it is shown that a Krylov–Uzawa iteration produces superlinear convergence on smooth domains, and estimation is given on its speed.

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44

ASANO, YUHMA, HIKARU KAWAI, and ASATO TSUCHIYA. "FACTORIZATION OF THE EFFECTIVE ACTION IN THE IIB MATRIX MODEL." International Journal of Modern Physics A 27, no. 17 (2012): 1250089. http://dx.doi.org/10.1142/s0217751x12500893.

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We study the low-energy effective action of the IIB matrix model in the derivative interpretation, where the diffeomorphism invariance is manifest and arbitrary manifolds are described by matrices. We show that it is expressed as a sum of terms, each of which is factorized into a product of diffeomorphism invariant action functionals: [Formula: see text]. Each action functional si is an ordinary local action of the form [Formula: see text], where Oi(x) is a scalar operator. This is also true for the background consisting of block diagonal matrices. In this case, the effective action can be int

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45

Liu, Jie, Jun ie Huang, and Alatancang Chen. "Semigroup generations of unbounded block operator matrices based on the space decomposition." Operators and Matrices, no. 2 (2020): 295–304. http://dx.doi.org/10.7153/oam-2020-14-23.

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46

Kraus, Margarita, Matthias Langer, and Christiane Tretter. "Variational principles and eigenvalue estimates for unbounded block operator matrices and applications." Journal of Computational and Applied Mathematics 171, no. 1-2 (2004): 311–34. http://dx.doi.org/10.1016/j.cam.2004.01.024.

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47

GrubisÌicÌ, Luka. "On relative perturbation theory for eigenvalues and eigenvectors of block operator matrices." PAMM 7, no. 1 (2007): 2050001–2. http://dx.doi.org/10.1002/pamm.200700013.

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48

Jeribi, Aref, Bilel Krichen, and Ali Zitouni. "Properties of Demicompact Operators, Essential Spectra and Some Perturbation Results for Block Operator Matrices with Applications." Linear and Multilinear Algebra 68, no. 12 (2019): 2506–22. http://dx.doi.org/10.1080/03081087.2019.1586826.

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49

Deng, Chun Yuan, and Hong Ke Du. "REPRESENTATIONS OF THE MOORE-PENROSE INVERSE OF 2×2 BLOCK OPERATOR VALUED MATRICES." Journal of the Korean Mathematical Society 46, no. 6 (2009): 1139–50. http://dx.doi.org/10.4134/jkms.2009.46.6.1139.

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50

Lindsay Orr, John. "An estimate on the norm of the product of infinite block operator matrices." Journal of Combinatorial Theory, Series A 63, no. 2 (1993): 195–209. http://dx.doi.org/10.1016/0097-3165(93)90056-e.

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