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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 10 scientific papers (total in 10 papers)

Topological Radicals and Joint Spectral Radius

Yu. V. Turovskiia, V. S. Shulmanb

a Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku
b Vologda State Technical University
Full-text PDF (286 kB) Citations (10)
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DOI: https://doi.org/10.4213/faa3089
Abstract: It is shown that the joint spectral radius ρ(M) of a precompact set M of operators on a Banach space equals the maximum of two numbers, the joint spectral radius ρe(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
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/faa/v46/i4/p61
    • This publication is cited in the following 10 articles:
    1. Edward Kissin, Victor S. Shulman, Yurii V. Turovskii, “Topological radicals, IX: relations in ideals of C*-algebras”, Ann. Funct. Anal., 16:1 (2025)  crossref
    2. 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)  crossref
    3. 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)  crossref
    4. E. Kissin, Yu. V. Turovskii, V. S. Shulman, “On the Theory of Topological Radicals”, J Math Sci, 263:6 (2022), 805  crossref
    5. Magiatis Ch., “Characterizations of Elementary Operators”, Oper. Matrices, 15:4 (2021), 1469–1475  crossref  mathscinet  isi
    6. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. 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  mathnet  crossref
    8. G. Andreolas, M. Anoussis, “Topological radicals of nest algebras”, Studia Math., 237:2 (2017), 177–184  crossref  mathscinet  zmath  isi  scopus
    9. P. Cao, Yu. V. Turovskii, “Topological radicals, VI. Scattered elements in Banach Jordan and associative algebras”, Studia Math., 235:2 (2016), 171–208  crossref  mathscinet  zmath  isi  elib  scopus
    10. 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  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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