The spectrally bounded linear maps on operator algebras

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

Abstrakty

EN

We show that every spectrally bounded linear map Φ from a Banach algebra onto a standard operator algebra acting on a complex Banach space is square-zero preserving. This result is used to show that if Φ₂ is spectrally bounded, then Φ is a homomorphism multiplied by a nonzero complex number. As another application to the Hilbert space case, a classification theorem is obtained which states that every spectrally bounded linear bijection Φ from ℬ(H) onto ℬ(K), where H and K are infinite-dimensional complex Hilbert spaces, is either an isomorphism or an anti-isomorphism multiplied by a nonzero complex number. If Φ is not injective, then Φ vanishes at all compact operators.

Kategorie tematyczne

• 47B48: Operators on Banach algebras
• 47L10: Algebras of operators on Banach spaces and other topological linear spaces
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 150
• Numer: 3
• Strony: 261-271

Daty

wydano

2002

Twórcy

autor

Jianlian Cui

• Jianlian Cui, Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, P.R. China
• Department of Applied Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R. China
• Department of Mathematics, Shanxi Teachers University, Linfen 041004, P.R. China

autor

Jinchuan Hou

• Jinchuan Hou, Department of Mathematics, Shanxi Teachers University, Linfen 041004, P.R. China
• Department of Mathematics, Shanxi University, Taiyuan 030000, P. R. China

Identyfikatory

DOI

10.4064/sm150-3-4