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Funktsional'nyi Analiz i ego Prilozheniya, 2018, Volume 52, Issue 1, Pages 65–69
DOI: https://doi.org/10.4213/faa3454 (Mi faa3454) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

Invariant Subspaces for Commuting Operators on a Real Banach Space

V. I. Lomonosova, V. S. Shul'manb

a Department of Mathematics, Kent State University, Kent, USA
b Department of Higher Mathematics, Vologda State University, Vologda, Russia
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DOI: https://doi.org/10.4213/faa3454
Abstract: It is proved that the commutative algebra $\mathcal{A}$ of operators on a reflexive real Banach space has an invariant subspace if each operator $T\in\mathcal{A}$ satisfies the condition
$$ \|1-\varepsilon T^2\|_e\le 1+o(\varepsilon)\ \text{as}\ \varepsilon\searrow 0 $$
where $\|\cdot\|_e$ denotes the essential norm. This implies the existence of an invariant subspace for any commutative family of essentially self-adjoint operators on a real Hilbert space.
Keywords: Banach space, algebra of operators, invariant subspace.
Received: 09.11.2016
English version:
Functional Analysis and Its Applications, 2018, Volume 52, Issue 1, Pages 53–56
DOI: https://doi.org/10.1007/s10688-018-0207-6
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: V. I. Lomonosov, V. S. Shul'man, “Invariant Subspaces for Commuting Operators on a Real Banach Space”, Funktsional. Anal. i Prilozhen., 52:1 (2018), 65–69; Funct. Anal. Appl., 52:1 (2018), 53–56
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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