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

Research output: Contribution to journalArticle

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
Publication statusPublished - Jan 1 1999

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Linear Preserver
Mathematical operators
Linear map
Operator
Set theory
Algebra
Preserver
Partial Isometry
Operator Algebras
Finite Rank
Idempotent
Continuation
Projection
Subset
Form

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis

Cite this

Some linear preserver problems on B(H) concerning rank and corank. / Molnár, L.

In: Linear Algebra and Its Applications, Vol. 286, No. 1-3, 01.01.1999, p. 311-321.

Research output: Contribution to journalArticle

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