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Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 1, Pages 65–69 (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

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
$$ \|1-\varepsilon T^2\|_e\le 1+o(\varepsilon) as \varepsilon\searrow 0 $$
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.

DOI: https://doi.org/10.4213/faa3454

Full text: PDF file (131 kB)
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English version:
Functional Analysis and Its Applications, 2018, 52:1, 53–56

Bibliographic databases:

UDC: 517
Received: 09.11.2016

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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\paper Invariant Subspaces for Commuting Operators on a Real Banach Space
\jour Funktsional. Anal. i Prilozhen.
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\vol 52
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\pages 65--69
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\vol 52
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\pages 53--56
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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