Linear maps preserving elements annihilated by the polynomial $XY-YX^{†}$

• Autorzy: Jianlian Cui , Jinchuan Hou
• Języki publikacji: EN

Abstrakty

EN

Let H and K be complex complete indefinite inner product spaces, and ℬ(H,K) (ℬ(H) if K = H) the set of all bounded linear operators from H into K. For every T ∈ ℬ(H,K), denote by $T^{†}$ the indefinite conjugate of T. Suppose that Φ: ℬ(H) → ℬ(K) is a bijective linear map. We prove that Φ satisfies $Φ(A)Φ(B) = Φ(B)Φ(A)^{†}$ for all A, B ∈ ℬ(H) with $AB = BA^{†}$ if and only if there exist a nonzero real number c and a generalized indefinite unitary operator U ∈ ℬ(H,K) such that $Φ(A) = cUAU^{†}$ for all A ∈ ℬ(H).

Kategorie tematyczne

• 47B48: Operators on Banach algebras
• 47B50: Operators on spaces with an indefinite metric

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 174
• Numer: 2
• Strony: 183-199

Daty

wydano

2006

Twórcy

autor

Jianlian Cui

• Department of Mathematical Science, University of Tsinghua, Beijing, 100084, P.R. China

autor

Jinchuan Hou

• Department of Applied Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R. China
• Department of Mathematics, Shanxi Teachers University, Linfen, 041004, P.R. China

Identyfikatory

DOI

10.4064/sm174-2-5