Jordan isomorphisms and maps preserving spectra of certain operator products

• Autorzy: Jinchuan Hou , Chi-Kwong Li , Ngai-Ching Wong
• Języki publikacji: EN

Abstrakty

EN

Let 𝓐₁, 𝓐₂ be (not necessarily unital or closed) standard operator algebras on locally convex spaces X₁, X₂, respectively. For k ≥ 2, consider different products $T₁ ∗ ⋯ ∗ T_{k}$ on elements in $𝓐_{i}$, which covers the usual product $T₁ ∗ ⋯ ∗ T_{k} = T₁ ⋯ T_{k}$ and the Jordan triple product T₁ ∗ T₂ = T₂T₁T₂. Let Φ: 𝓐₁ → 𝓐₂ be a (not necessarily linear) map satisfying $σ(Φ(A₁) ∗ ⋯ ∗ Φ(A_{k})) = σ(A₁ ∗ ⋯ ∗ A_{k})$ whenever any one of $A_{i}$'s has rank at most one. It is shown that if the range of Φ contains all rank one and rank two operators then Φ must be a Jordan isomorphism multiplied by a root of unity. Similar results for self-adjoint operators acting on Hilbert spaces are obtained.

Kategorie tematyczne

• 47B49: Transformers, preservers (operators on spaces of operators)
• 47A12: Numerical range, numerical radius

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 184
• Numer: 1
• Strony: 31-47

Daty

wydano

2008

Twórcy

autor

Jinchuan Hou

• Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R. of China

autor

Chi-Kwong Li

• Department of Mathematics, The College of William & Mary, Williamsburg, VA 13185, U.S.A.

autor

Ngai-Ching Wong

• Department of Applied Mathematics, National Sun Yat-sen University, and National Center for Theoretical Sciences, Kaohsiung 80424, Taiwan
• Department of Mathematics, The Chinese University of Hong Kong, Hong Kong

Identyfikatory

DOI

10.4064/sm184-1-2