On the Banach-Stone problem

• Autorzy: Jyh-Shyang Jeang , Ngai-Ching Wong
• Języki publikacji: EN

Abstrakty

EN

Let X and Y be locally compact Hausdorff spaces, let E and F be Banach spaces, and let T be a linear isometry from C₀(X,E) into C₀(Y,F). We provide three new answers to the Banach-Stone problem: (1) T can always be written as a generalized weighted composition operator if and only if F is strictly convex; (2) if T is onto then T can be written as a weighted composition operator in a weak sense; and (3) if T is onto and F does not contain a copy of $ℓ₂^{∞}$ then T can be written as a weighted composition operator in the classical sense.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46E40: Spaces of vector- and operator-valued functions
• 46B04: Isometric theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 155
• Numer: 2
• Strony: 95-105

Daty

wydano

2003

Twórcy

autor

Jyh-Shyang Jeang

• Institute of Mathematics, Academia Sinica, Taipei, Taiwan 11529, Republic of China

autor

Ngai-Ching Wong

• Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 80424, Republic of China

Identyfikatory

DOI

10.4064/sm155-2-1