Weak∗-Polish Banach spaces

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 Uniform Rotundity of Banach Spaces

1. Definitions and preliminaries. In this note, X and Y denote Banach spaces and X∗ and Y∗ denote the conjugate spaces of X and Y , respectively. Let A⊂X be a closed subset and X/A denote the quotient space. We use S(X) for the unit sphere in X and Plp (Xi) for the lp product space. We refer to [1, 3] for the following definitions and notations. For more recent treatment, one may see, for examp...

Weak convergence theorem for Lipschitzian pseudocontraction semigroups in Banach spaces

In this work, theorems of weak convergence of an implicit iterative algorithm with errors for treating a nonexpansive semigroup and a Lipschitzian pseudocontractive semigroup are estabilshed in the framework of real Banach spaces. 2010 Mathematics Subject Classification. Primary 60J05; Secondary 60J20.