Yu. V. Turovskii, V. S. Shulman, “Topological Radicals and Joint Spectral Radius”, Funktsional. Anal. i Prilozhen., 46:4 (2012), 61–82; Funct. Anal. Appl., 46:4 (2012), 287

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Funktsional'nyi Analiz i ego Prilozheniya, 2012, Volume 46, Issue 4, Pages 61–82
DOI: https://doi.org/10.4213/faa3089 (Mi faa3089)

This article is cited in 11 scientific papers (total in 11 papers)

Topological Radicals and Joint Spectral Radius

Yu. V. Turovskii^a, V. S. Shulman^b

^a Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku
^b Vologda State Technical University

Full-text PDF (286 kB) Citations (11)

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DOI: https://doi.org/10.4213/faa3089

Abstract: It is shown that the joint spectral radius $\rho(M)$ of a precompact set $M$ of operators on a Banach space equals the maximum of two numbers, the joint spectral radius $\rho_{e}(M)$ of the image of $M$ in the Calkin algebra and the BW-radius $r(M)$. Similar results related to general normed algebras are also obtained. The proofs are based on the theory of topological radicals of normed algebras.

Keywords: joint spectral radius, the Berger–Wang formula, topological radical, invariant subspace.

Received: 20.11.2010

English version:
Functional Analysis and Its Applications, 2012, Volume 46, Issue 4, Pages 287–304
DOI: https://doi.org/10.1007/s10688-012-0036-y

Bibliographic databases:

Document Type: Article

UDC: 517.986.22

Language: Russian

Citation: Yu. V. Turovskii, V. S. Shulman, “Topological Radicals and Joint Spectral Radius”, Funktsional. Anal. i Prilozhen., 46:4 (2012), 61–82; Funct. Anal. Appl., 46:4 (2012), 287–304

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Linking options:

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https://www.mathnet.ru/eng/faa/v46/i4/p61

This publication is cited in the following 11 articles:

Edward Kissin, Victor S. Shulman, Yurii V. Turovskii, “Topological radicals, IX: relations in ideals of C*-algebras”, Ann. Funct. Anal., 16:1 (2025)
H. Arroussi, C. Tong, J. A. Virtanen, Z. Yuan, “Volterra-type inner derivations on Hardy spaces”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 119:2 (2025)
Xueyan Yang, Hua He, Cezhong Tong, Hicham Arroussi, “Volterra and Composition Inner Derivations on the Fock–Sobolev Spaces”, Complex Anal. Oper. Theory, 18:5 (2024)
Hua He, Xueyan Yang, Zicong Yang, “Composition and Volterra-type inner derivations on the generalized Fock spaces”, Filomat, 38:11 (2024), 3707
E. Kissin, Yu. V. Turovskii, V. S. Shulman, “On the Theory of Topological Radicals”, J Math Sci, 263:6 (2022), 805
Magiatis Ch., “Characterizations of Elementary Operators”, Oper. Matrices, 15:4 (2021), 1469–1475
V. I. Lomonosov, V. S. Shulman, “Halmos problems and related results in the theory of invariant subspaces”, Russian Math. Surveys, 73:1 (2018), 31–90
E. V. Kissin, Yu. V. Turovskii, V. S. Shulman, “O teorii topologicheskikh radikalov”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 64, no. 3, Rossiiskii universitet druzhby narodov, M., 2018, 490–546
G. Andreolas, M. Anoussis, “Topological radicals of nest algebras”, Studia Math., 237:2 (2017), 177–184
P. Cao, Yu. V. Turovskii, “Topological radicals, VI. Scattered elements in Banach Jordan and associative algebras”, Studia Math., 235:2 (2016), 171–208
V. S. Shulman, Yu. V. Turovskii, “Topological radicals, V. From algebra to spectral theory”, Algebraic methods in functional analysis, Oper. Theory Adv. Appl., 233, Birkhäuser/Springer, Basel, 2014, 171–280

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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