Linear maps preserving quasi-commutativity

• Autorzy: Heydar Radjavi , Peter Šemrl
• Języki publikacji: EN

Abstrakty

EN

Let X and Y be Banach spaces and ℬ(X) and ℬ(Y) the algebras of all bounded linear operators on X and Y, respectively. We say that A,B ∈ ℬ(X) quasi-commute if there exists a nonzero scalar ω such that AB = ωBA. We characterize bijective linear maps ϕ : ℬ(X) → ℬ(Y) preserving quasi-commutativity. In fact, such a characterization can be proved for much more general algebras. In the finite-dimensional case the same result can be obtained without the bijectivity assumption.

Kategorie tematyczne

• 47B49: Transformers, preservers (operators on spaces of operators)
• 15A27: Commutativity
• 15A04: Linear transformations, semilinear transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 184
• Numer: 2
• Strony: 191-204

Daty

wydano

2008

Twórcy

autor

Heydar Radjavi

• Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada N2L 3G1

autor

Peter Šemrl

• Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

Identyfikatory

DOI

10.4064/sm184-2-7