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Journal articles on the topic 'Strictly singular operators'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Cobos, F., A. Manzano, A. Martínez, and P. Matos. "On interpolation of strictly singular operators, strictly co-singular operators and related operator ideals." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 5 (2000): 971–89. http://dx.doi.org/10.1017/s0308210500000524.

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2

Cross, R. W. "Unbounded strictly singular operators." Indagationes Mathematicae (Proceedings) 91, no. 3 (1988): 245–48. http://dx.doi.org/10.1016/s1385-7258(88)80004-0.

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3

Kizgut, Ersin, and Murat Yurdakul. "Remarks on strictly singular operators." International Journal of Mathematical Analysis 11 (2017): 883–90. http://dx.doi.org/10.12988/ijma.2017.77103.

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4

Lindström, Mikael, Eero Saksman, and Hans-Olav Tylli. "Strictly Singular and Cosingular Multiplications." Canadian Journal of Mathematics 57, no. 6 (2005): 1249–78. http://dx.doi.org/10.4153/cjm-2005-050-7.

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AbstractLet L(X) be the space of bounded linear operators on the Banach space X. We study the strict singularity and cosingularity of the two-sidedmultiplication operators S ↦ ASB on L(X), where A, B ∈ L(X) are fixed bounded operators and X is a classical Banach space. Let 1 < p < ∞and p ≠ 2. Our main result establishes that the multiplication S ↦ ASB is strictly singular on L(Lp(0, 1)) if and only if the non-zero operators A, B ∈ L(Lp(0, 1)) are strictly singular. We also discuss the case where X is a L1- or a L∞-space, as well as several other relevant examples.

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5

Ganesa Moorthy, C., and C. T. Ramasamy. "Characterizations of Strong Strictly Singular Operators." Chinese Journal of Mathematics 2013 (December 25, 2013): 1–4. http://dx.doi.org/10.1155/2013/834637.

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A new class of operators called strong strictly singular operators on normed spaces is introduced. This class includes the class of precompact operators, and is contained in the class of strictly singular operators. Some properties and characterizations for these operators are derived.

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6

Flores, J., F. L. Hernandez, and P. Tradacete. "POWERS OF OPERATORS DOMINATED BY STRICTLY SINGULAR OPERATORS." Quarterly Journal of Mathematics 59, no. 3 (2007): 321–34. http://dx.doi.org/10.1093/qmath/ham050.

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7

Ji-Shou, Ruan. "Invariant Subspace of Strictly Singular Operators." Proceedings of the American Mathematical Society 108, no. 4 (1990): 931. http://dx.doi.org/10.2307/2047948.

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8

del Amo, A. García, F. L. Hernández, and C. Ruiz. "Disjointly strictly singular operators and interpolation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 126, no. 5 (1996): 1011–26. http://dx.doi.org/10.1017/s0308210500023222.

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Interpolation properties of the class of disjointly strictly singular operators on Banach lattices are studied. We also give some applications to compare the lattice structure of two rearrangement invariant function spaces. In particular, we obtain suitable analytic characterisations of when the inclusion map between two Orlicz function spaces is disjointly strictly singular.

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9

Flores, Julio, and Francisco L. Hernández. "Domination by Positive Strictly Singular Operators." Journal of the London Mathematical Society 66, no. 2 (2002): 433–52. http://dx.doi.org/10.1112/s0024610702003447.

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10

Odell, Edward, and Ricardo V. Teixeira. "On S$_1$-strictly singular operators." Proceedings of the American Mathematical Society 143, no. 11 (2015): 4745–57. http://dx.doi.org/10.1090/proc/12452.

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11

Hernández and Semenov. "Strictly Singular Operators on Banach Lattices." Real Analysis Exchange 44, no. 1 (2019): 37. http://dx.doi.org/10.14321/realanalexch.44.1.0037.

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12

Ruan, Ji Shou. "Invariant subspace of strictly singular operators." Proceedings of the American Mathematical Society 108, no. 4 (1990): 931. http://dx.doi.org/10.1090/s0002-9939-1990-1002160-4.

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13

Flores, Julio. "Strictly Singular and Regular Integral Operators." Integral Equations and Operator Theory 55, no. 4 (2005): 487–96. http://dx.doi.org/10.1007/s00020-005-1399-8.

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14

AIENA, PIETRO, MANUEL GONZÁLEZ, and ANTONIO MARTÍNEZ-ABEJÓN. "CHARACTERIZATIONS OF STRICTLY SINGULAR AND STRICTLY COSINGULAR OPERATORS BY PERTURBATION CLASSES." Glasgow Mathematical Journal 54, no. 1 (2011): 87–96. http://dx.doi.org/10.1017/s0017089511000346.

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AbstractWe consider a class of operators that contains the strictly singular operators and it is contained in the perturbation class of the upper semi-Fredholm operators PΦ+. We show that this class is strictly contained in PΦ+, solving a question of Friedman. We obtain similar results for the strictly cosingular operators and the perturbation class of the lower semi-Fredholm operators PΦ−. We also characterize in terms of PΦ+ and in terms of PΦ−. As a consequence, we show that and are the biggest operator ideals contained in PΦ+ and PΦ−, respectively.

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15

Abbott, Catherine, Elizabeth Bator, and Paul Lewis. "Strictly singular and strictly cosingular operators on spaces of continuous functions." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 3 (1991): 505–21. http://dx.doi.org/10.1017/s0305004100070584.

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In this paper we will be concerned with studying operators T: C(K, X) → Y defined on Banach spaces of continuous functions. We will be particularly interested in studying the classes of strictly singular and strictly cosingular operators. In the process, we obtain answers to certain questions recently raised by Bombal and Porras in [5]. Specifically, we study Banach space X and Y for which an operator T: C(K, X) → Y with representing measure m is strictly singular (strictly cosingular) whenever m is strongly bounded and m(A) is strictly singular (strictly cosingular) for each Borel subset A of K. Along the way we establish several results dealing with non-compact operators on continuous function spaces, and we consolidate numerous results concerning extension theorems for operators defined on these same spaces. Also, we join Saab and Saab [25] in demonstrating that if l1 does not embed in X* then the adjoint T* of a strongly bounded map must be weakly precompact, thereby presenting an alternative solution to a question raised in [2].

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16

Bombal, F., and B. Porras. "Strictly Singular and Strictly Cosingular Operators on C(K, E)." Mathematische Nachrichten 143, no. 1 (1989): 355–64. http://dx.doi.org/10.1002/mana.19891430125.

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17

Tradacete, Pedro. "Spectral properties of disjointly strictly singular operators." Journal of Mathematical Analysis and Applications 395, no. 1 (2012): 376–84. http://dx.doi.org/10.1016/j.jmaa.2012.05.051.

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18

Flores, Julio, and Francisco L. Hernández. "Domination by positive disjointly strictly singular operators." Proceedings of the American Mathematical Society 129, no. 7 (2000): 1979–86. http://dx.doi.org/10.1090/s0002-9939-00-05948-7.

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19

Argyros, Spiros A., Kevin Beanland, and Pavlos Motakis. "Strictly singular operators in Tsirelson like spaces." Illinois Journal of Mathematics 57, no. 4 (2013): 1173–217. http://dx.doi.org/10.1215/ijm/1417442566.

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20

Meyer, Michael J. "Ideals of operators strictly singular on subspaces." Proceedings of the American Mathematical Society 122, no. 4 (1994): 1121. http://dx.doi.org/10.1090/s0002-9939-1994-1219729-8.

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21

Mathieu, Martin, та Pedro Tradacete. "Strictly singular multiplication operators on ℒ(X)". Israel Journal of Mathematics 236, № 2 (2020): 685–709. http://dx.doi.org/10.1007/s11856-020-1985-0.

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22

Chalendar, Isabelle, Emmanuel Fricain, Alexey I. Popov, Dan Timotin, and Vladimir G. Troitsky. "Finitely strictly singular operators between James spaces." Journal of Functional Analysis 256, no. 4 (2009): 1258–68. http://dx.doi.org/10.1016/j.jfa.2008.09.010.

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23

Dehici, Abdelkader, and Khaled Saoudi. "Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–10. http://dx.doi.org/10.1155/2007/26254.

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We show the existence of Banach spacesX,Ysuch that the set of strictly singular operators𝒮(X,Y)(resp., the set of strictly cosingular operators𝒞𝒮(X,Y))would be strictly included inℱ+(X,Y)(resp.,ℱ−(X,Y))for the nonempty class of closed densely defined upper semi-Fredholm operatorsΦ+(X,Y)(resp., for the nonempty class of closed densely defined lower semi-Fredholm operatorsΦ−(X,Y)).

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24

Beucher, O. J. "On interpolation of strictly (co-)singular linear operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 112, no. 3-4 (1989): 263–69. http://dx.doi.org/10.1017/s0308210500018734.

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SynopsisWe show that the property of linear operators to be in the surjective hull (injective hull) of the ideal of strictly singular (strictly cosingular) operators between Banach spaces is an interpolation property with respect to the real interpolation method with parameters 0 < ủ < 1 and < p < ℞.

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25

Read, C. "Strictly singular operators and the invariant subspace problem." Studia Mathematica 132, no. 3 (1999): 203–26. http://dx.doi.org/10.4064/sm-132-3-203-226.

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26

Flores, J., F. L. Hernández, N. J. Kalton, and P. Tradacete. "Characterizations of strictly singular operators on Banach lattices." Journal of the London Mathematical Society 79, no. 3 (2009): 612–30. http://dx.doi.org/10.1112/jlms/jdp007.

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27

Beanland, Kevin, and Pandelis Dodos. "ON STRICTLY SINGULAR OPERATORS BETWEEN SEPARABLE BANACH SPACES." Mathematika 56, no. 2 (2010): 285–304. http://dx.doi.org/10.1112/s0025579310001014.

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28

Hernández, Francisco L., Evgeny M. Semenov, and Pedro Tradacete. "Strictly singular operators on $L_p$ spaces and interpolation." Proceedings of the American Mathematical Society 138, no. 02 (2009): 675–86. http://dx.doi.org/10.1090/s0002-9939-09-10089-8.

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29

Flores, Julio. "Some Remarks on Disjointly Strictly Singular Positive Operators." Positivity 9, no. 3 (2005): 385–96. http://dx.doi.org/10.1007/s11117-004-0733-8.

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30

Androulakis, G., P. Dodos, G. Sirotkin, and V. G. Troitsky. "Classes of strictly singular operators and their products." Israel Journal of Mathematics 169, no. 1 (2008): 221–50. http://dx.doi.org/10.1007/s11856-009-0010-4.

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31

Androulakis, George, and Kevin Beanland. "Descriptive Set Theoretic Methods Applied to Strictly Singular and Strictly Cosingular Operators." Quaestiones Mathematicae 31, no. 2 (2008): 151–61. http://dx.doi.org/10.2989/qm.2008.31.2.4.476.

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32

Gurarie, David. "Finite propagation speed and kernels of strictly elliptic operators." International Journal of Mathematics and Mathematical Sciences 8, no. 1 (1985): 75–91. http://dx.doi.org/10.1155/s0161171285000072.

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We establish estimates of the resolvent and other related kernels and discussLp-theory for a class of strictly elliptic operators onRn. The class of operators considered in the paper is of the formA0+Bwith the leading elliptic partA0and a singular perturbationB, whose coefficients haveLp-type and are modeled after Schrödinger operators.

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33

Castillo, Jesús M. F., Marilda Simoes, and Jesús Suárez de la Fuente. "On a Question of Pełczyński about Strictly Singular Operators." Bulletin of the Polish Academy of Sciences Mathematics 60, no. 1 (2012): 27–36. http://dx.doi.org/10.4064/ba60-1-3.

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34

Kutzarova, Denka, Antonis Manoussakis, and Anna Pelczar-Barwacz. "Isomorphisms and strictly singular operators in mixed Tsirelson spaces." Journal of Mathematical Analysis and Applications 388, no. 2 (2012): 1040–60. http://dx.doi.org/10.1016/j.jmaa.2011.10.053.

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35

Semenov, E. M., P. Tradacete, and F. L. Hernandez. "Strictly singular operators in pairs of L p space." Doklady Mathematics 94, no. 1 (2016): 450–52. http://dx.doi.org/10.1134/s1064562416040281.

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36

Pelczar-Barwacz, Anna. "Strictly singular operators in asymptotic $\ell_{p}$ Banach spaces." Illinois Journal of Mathematics 56, no. 3 (2012): 861–83. http://dx.doi.org/10.1215/ijm/1391178553.

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37

Androulakis, George, and Per Enflo. "A property of strictly singular one-to-one operators." Arkiv för Matematik 41, no. 2 (2003): 233–52. http://dx.doi.org/10.1007/bf02390813.

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38

Mykhaylyuk, V., M. Popov, B. Randrianantoanina та G. Schechtman. "Narrow and ℓ2-strictly singular operators from L p". Israel Journal of Mathematics 203, № 1 (2014): 81–108. http://dx.doi.org/10.1007/s11856-014-0012-8.

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39

Flores, Julio, Francisco L. Hernández, Evgueni M. Semenov, and Pedro Tradacete. "Strictly singular and power-compact operators on Banach lattices." Israel Journal of Mathematics 188, no. 1 (2011): 323–52. http://dx.doi.org/10.1007/s11856-011-0152-z.

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40

Álvarez, Teresa, and Diane Wilcox. "Perturbation theory of multivalued atkinson operators in normed spaces." Bulletin of the Australian Mathematical Society 76, no. 2 (2007): 195–204. http://dx.doi.org/10.1017/s0004972700039587.

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We prove several stability results for Atkinson linear relations under additive perturbation by small norm, strictly singular and strictly cosingular multivalued linear operators satisfying some additional conditions.

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41

ÁLVAREZ, T. "STRICTLY SINGULAR PERTURBATION OF ALMOST SEMI-FREDHOLM LINEAR RELATIONS IN NORMED SPACES." Glasgow Mathematical Journal 56, no. 1 (2013): 211–19. http://dx.doi.org/10.1017/s0017089513000189.

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AbstractIn this paper, we introduce the notions of almost upper semi-Fredholm and strictly singular pairs of subspaces and show that the class of almost upper semi-Fredholm pairs of subspaces is stable under strictly singular pairs perturbation. We apply this perturbation result to investigate the stability of almost semi-Fredholm multi-valued linear operators in normed spaces under strictly singular perturbation as well as the behaviour of the index under perturbation.

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42

González, Manuel. "On the duality problem for weakly compact, strictly singular operators." Quaestiones Mathematicae 28, no. 1 (2005): 37–38. http://dx.doi.org/10.2989/16073600509486113.

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43

Gasparis, I. "Strictly singular non-compact operators on hereditarily indecomposable Banach spaces." Proceedings of the American Mathematical Society 131, no. 4 (2002): 1181–89. http://dx.doi.org/10.1090/s0002-9939-02-06657-1.

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44

Flores, Julio, Francisco L. Hernández, and Pedro Tradacete. "Domination problems for strictly singular operators and other related classes." Positivity 15, no. 4 (2010): 595–616. http://dx.doi.org/10.1007/s11117-010-0100-x.

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45

Beanland, Kevin. "An ordinal indexing on the space of strictly singular operators." Israel Journal of Mathematics 182, no. 1 (2011): 47–59. http://dx.doi.org/10.1007/s11856-011-0023-7.

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46

Flores, Julio, Pedro Tradacete, and Vladimir G. Troitsky. "Invariant subspaces of positive strictly singular operators on Banach lattices." Journal of Mathematical Analysis and Applications 343, no. 2 (2008): 743–51. http://dx.doi.org/10.1016/j.jmaa.2008.01.067.

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47

Lefèvre, Pascal, and Luis Rodríguez-Piazza. "Finitely strictly singular operators in harmonic analysis and function theory." Advances in Mathematics 255 (April 2014): 119–52. http://dx.doi.org/10.1016/j.aim.2013.12.034.

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48

Hernández, Francisco L., Evgeny M. Semenov, and Pedro Tradacete. "Interpolation and extrapolation of strictly singular operators between L spaces." Advances in Mathematics 316 (August 2017): 667–90. http://dx.doi.org/10.1016/j.aim.2017.06.028.

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49

Manoussakis, Antonis, and Anna Pelczar-Barwacz. "Strictly singular non-compact operators on a class of HI spaces." Bulletin of the London Mathematical Society 45, no. 3 (2012): 463–82. http://dx.doi.org/10.1112/blms/bds111.

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50

Latrach, Khalid, and Abdelkader Dehici. "Relatively Strictly Singular Perturbations, Essential Spectra, and Application to Transport Operators." Journal of Mathematical Analysis and Applications 252, no. 2 (2000): 767–89. http://dx.doi.org/10.1006/jmaa.2000.7121.

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