A condition for a subspace of ℬ(H) to be an ideal

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Abstract

Let H be a real or complex Hilbert space with dim H > 1. The subspace A ⊂ ℬ(H) is an ideal if and only if TA - AT* ∈ for every T ∈ ℬ(H), A ∈ A. Every element of ℬ(H) is the finite sum of TA - AT* type operators.

Original languageEnglish
Pages (from-to)229-234
Number of pages6
JournalLinear Algebra and Its Applications
Volume235
DOIs
Publication statusPublished - Mar 1 1996

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ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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