Some linear preserver problems on B(H) concerning rank and corank

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8 Citations (Scopus)

Abstract

As a continuation of the work on linear maps between operator algebras which preserve certain subsets of operators with finite rank, or finite corank, here we consider the problem inbetween, that is, we treat the question of preserving operators with infinite rank and infinite corank. Since, as it turns out, in this generality our preservers cannot be written in a nice form what we have got used to when dealing with linear preserver problems, hence we restrict our attention to certain important classes of operators like idempotents, or projections, or partial isometries. We conclude the paper with a result on the form of linear maps which preserve the left ideals in B(H).

Original languageEnglish
Pages (from-to)311-321
Number of pages11
JournalLinear Algebra and Its Applications
Volume286
Issue number1-3
DOIs
Publication statusPublished - Jan 1 1999

Keywords

  • Idempotents
  • Linear preservers
  • One-sided ideals
  • Partial isometries
  • Projections

ASJC Scopus subject areas

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

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