Weak Baire measurability of the balls in a Banach space

• Autorzy: José Rodríguez
• Języki publikacji: EN

Abstrakty

EN

Let X be a Banach space. The property (∗) "the unit ball of X belongs to Baire(X, weak)" holds whenever the unit ball of X* is weak*-separable; on the other hand, it is also known that the validity of (∗) ensures that X* is weak*-separable. In this paper we use suitable renormings of $ℓ^{∞}(ℕ)$ and the Johnson-Lindenstrauss spaces to show that (∗) lies strictly between the weak*-separability of X* and that of its unit ball. As an application, we provide a negative answer to a question raised by K. Musiał.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 28B05: Vector-valued set functions, measures and integrals
• 46G10: Vector-valued measures and integration
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 185
• Numer: 2
• Strony: 169-176

Daty

wydano

2008

Twórcy

autor

José Rodríguez

• Departamento de Análisis Matemático, Universidad de Valencia, Avda. Doctor Moliner 50, 46100 Burjassot, Valencia, Spain
• Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia. Spain

Identyfikatory

DOI

10.4064/sm185-2-5