Similarity invariant subspaces and lie ideals in operator algebras

G. Belitskii; A. Markus

doi:10.1007/BF01217529

Similarity invariant subspaces and lie ideals in operator algebras

G. Belitskii, A. Markus

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

We study subspaces of algebra L(X) which are invariant with respect to all similarity transformations and give a full description of these subspaces for finite-dimensional space X, for separable Hilbert space X and for X = l^p (1 ≤ p < ∞) or c₀. The problem is equivalent to a study of Lie ideals in L(X).

Original language	English
Pages (from-to)	127-137
Number of pages	11
Journal	Integral Equations and Operator Theory
Volume	44
Issue number	2
DOIs	https://doi.org/10.1007/BF01217529
State	Published - 3 Dec 2002

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/BF01217529

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title = "Similarity invariant subspaces and lie ideals in operator algebras",

abstract = "We study subspaces of algebra L(X) which are invariant with respect to all similarity transformations and give a full description of these subspaces for finite-dimensional space X, for separable Hilbert space X and for X = lp (1 ≤ p < ∞) or c0. The problem is equivalent to a study of Lie ideals in L(X).",

author = "G. Belitskii and A. Markus",

note = "Funding Information: *Partially supported by Israel Science Foundation, Grant 216/98.",

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AU - Markus, A.

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Y1 - 2002/12/3

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AB - We study subspaces of algebra L(X) which are invariant with respect to all similarity transformations and give a full description of these subspaces for finite-dimensional space X, for separable Hilbert space X and for X = lp (1 ≤ p < ∞) or c0. The problem is equivalent to a study of Lie ideals in L(X).

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JF - Integral Equations and Operator Theory

IS - 2

ER -

Similarity invariant subspaces and lie ideals in operator algebras

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