Similarity-preserving linear maps on B(X)

• Autorzy: Fangyan Lu , Chaoran Peng
• Języki publikacji: EN

Abstrakty

EN

Let X be an infinite-dimensional Banach space, and B(X) the algebra of all bounded linear operators on X. Then ϕ: B(X) → B(X) is a bijective similarity-preserving linear map if and only if one of the following holds:
(1) There exist a nonzero complex number c, an invertible bounded operator T in B(X) and a similarity-invariant linear functional h on B(X) with h(I) ≠ -c such that $ϕ(A) = cTAT^{-1} + h(A)I$ for all A ∈ B(X).
(2) There exist a nonzero complex number c, an invertible bounded linear operator T: X* → X and a similarity-invariant linear functional h on B(X) with h(I) ≠ -c such that $ϕ(A) = cTA*T^{-1} + h(A)I$ for all A ∈ B(X).

Kategorie tematyczne

• 47B49: Transformers, preservers (operators on spaces of operators)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 209
• Numer: 1
• Strony: 1-10

Daty

wydano

2012

Twórcy

autor

Fangyan Lu

• Department of Mathematics, Soochow University, Suzhou 215006, P.R. China

autor

Chaoran Peng

• Department of Mathematics, Soochow University, Suzhou 215006, P.R. China

Identyfikatory

DOI

10.4064/sm209-1-1