On localized weak precompactness in Banach spaces

A remark on localized weak precompactness in Banach spaces

We give a characterization of K-weakly precompact sets in terms of uniform Gateaux differentiability of certain continuous convex functions.

Weak Interpolation in Banach Spaces

Weak Thresholding Greedy Algorithms in Banach Spaces

We consider weak thresholding greedy algorithms with respect to Markushevich bases in general Banach spaces. We find sufficient conditions for the equivalence of boundedness and convergence of the approximants. We also show that if there is a weak thresholding algorithm for the system which gives the best n-term approximation up to a multiplicative constant, then the system is already “greedy”....

On Weak Exponential Expansiveness of Evolution Families in Banach Spaces

The aim of this paper is to give several characterizations for the property of weak exponential expansiveness for evolution families in Banach spaces. Variants for weak exponential expansiveness of some well-known results in stability theory (Datko (1973), Rolewicz (1986), Ichikawa (1984), and Megan et al. (2003)) are obtained.

On the Weak Relatively Nonexpansive Mappings in Banach Spaces