Linear rank and corank preserving maps on ℬ(H) and an application to *-semigroup isomorphisms of operator ideals

Máté Györy, L. Molnár, Peter Šemrl

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We characterize linear rank-k nonincreasing, rank-k preserving, and corank-k preserving maps on ℬ(H), the algebra of all bounded linear operators on the Hilbert space H. This unifies and extends finite-dimensional results and results on linear rank-1 nonincreasing and rank-1 preserving maps in the infinite-dimensional case. We conclude with an application to *-semigroup isomorphisms of operator ideals.

Original languageEnglish
Pages (from-to)253-266
Number of pages14
JournalLinear Algebra and Its Applications
Volume280
Issue number2-3
Publication statusPublished - Sep 4 1998

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Operator Ideals
Isomorphism
Semigroup
Hilbert spaces
Algebra
Mathematical operators
Bounded Linear Operator
Hilbert space

Keywords

  • *-Semigroup isomorphism
  • Linear rank preserver
  • Operator ideal

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis

Cite this

Linear rank and corank preserving maps on ℬ(H) and an application to *-semigroup isomorphisms of operator ideals. / Györy, Máté; Molnár, L.; Šemrl, Peter.

In: Linear Algebra and Its Applications, Vol. 280, No. 2-3, 04.09.1998, p. 253-266.

Research output: Contribution to journalArticle

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