Weak-star point of continuity property and Schauder bases

• Autorzy: Ginés López-Pérez , José A. Soler-Arias
• Języki publikacji: EN

Abstrakty

EN

We characterize the weak-star point of continuity property for subspaces of dual spaces with separable predual and we deduce that the weak-star point of continuity property is determined by subspaces with a Schauder basis in the natural setting of dual spaces of separable Banach spaces. As a consequence of the above characterization we show that a dual space has the Radon-Nikodym property if, and only if, every seminormalized topologically weak-star null tree has a boundedly complete branch, which improves some results of Dutta and Fonf (2008) obtained for the separable case. Also, as a consequence of the above characterization, the following result of Rosenthal (2007) is deduced: every seminormalized basic sequence in a Banach space with the point of continuity property has a boundedly complete subsequence.

Kategorie tematyczne

• 46B22: Radon-Nikod{\'y}m, Kre{\u\i}n-Milman and related properties
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 219
• Numer: 3
• Strony: 225-236

Daty

wydano

2013

Twórcy

autor

Ginés López-Pérez

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

autor

José A. Soler-Arias

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

Identyfikatory

DOI

10.4064/sm219-3-3