Banach spaces with many boundedly complete basic sequences failing PCP

López-Pérez, Ginés

doi:10.1016/j.jfa.2010.06.015

Search citation statements

Order By: Relevance

Paper Sections

Select...

Results1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2011

2013

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The converse of the above result is false, even for Banach spaces not containing ℓ 1 (see [5]). Now we pass to show some consequences about the problem of the determination of w * -PCP by subspaces with a basis.…”

Section: Resultsmentioning

confidence: 98%

Weak-star point of continuity property and Schauder bases

López-Pérez

Soler-Arias

2013

Studia Math.

View full text Add to dashboard Cite

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 get that a dual space satisfies the Radon-Nikodym property if, and only if, every seminormalized topologically weak-star null tree has a boundedly complete branch, which improves some results in [3] obtained for the separable case. Also, as a consequence of the above characterization, the following result obtained in [8] is deduced: every seminormalized basic sequence in a Banach space with the point of continuity property has a boundedly complete subsequence.

show abstract

Section: Resultsmentioning

confidence: 98%