36 citations · 60 across the 5 of their papers we have counts for
5 papers · 1 filter
On strongly norm attaining Lipschitz maps
Bernardo Cascales, Rafa Chiclana, Luis Garcia-Lirola +2
We study the set of those Lipschitz maps from a (complete pointed) metric space to a Banach space which (strongly) attain their Lipschitz norm (i.…
-flatness and Bishop-Phelps-Bollobás type theorems for operators
Bernardo Cascales, Antonio J. Guirao, Vladimir Kadets +1
The Bishop-Phelps-Bollobás property deals with simultaneous approximation of an operator and a vector at which nearly attains its norm by an operator and a vector…
One side James' Compactness Theorem
Bernardo Cascales, José Orihuela, Antonio Pérez
We present some extensions of classical results that involve elements of the dual of Banach spaces, such as Bishop-Phelp's theorem and James' compactness theorem, but restricting t…
A quantitative version of James' compactness theorem
Bernardo Cascales, Ondřej F. K. Kalenda, Jiří Spurný
We introduce two measures of weak non-compactness and that quantify, via distances, the idea of boundary behind James' compactness theorem. These measures tell us, for…
The Schur l1 Theorem for filters
Antonio Avilés, Bernardo Cascales, Vladimir Kadets +1
We study the classes of filters F on N such that the weak and strong F-convergence of sequences in l1 coincide. We study also an analogue of l1 weak sequential completeness theorem…