A bilinear version of Holsztyński's theorem on isometries of C(X)-spaces

• Autorzy: Antonio Moreno Galindo , Ángel Rodríguez Palacios
• Języki publikacji: EN

Abstrakty

EN

We prove that, for a compact metric space X not reduced to a point, the existence of a bilinear mapping ⋄: C(X) × C(X) → C(X) satisfying ||f⋄g|| = ||f|| ||g|| for all f,g ∈ C(X) is equivalent to the uncountability of X. This is derived from a bilinear version of Holsztyński's theorem [3] on isometries of C(X)-spaces, which is also proved in the paper.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46H70: Nonassociative topological algebras
• 46B04: Isometric theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 166
• Numer: 1
• Strony: 83-91

Daty

wydano

2005

Twórcy

autor

Antonio Moreno Galindo

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

autor

Ángel Rodríguez Palacios

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Identyfikatory

DOI

10.4064/sm166-1-6