Norm continuity of weakly continuous mappings into Banach spaces

Spaces of continuous functions into a Banach space

On Weakly Compact Subsets of Banach Spaces

Introduction. The two sections of this note are independent, but they are related by the fact that both use the results of [5 ] to obtain information on the properties of weakly compact sets in Banach spaces. In the first section we prove some results on a class of compact sets which is believed to include all weakly compact subsets of Banach spaces. We are interested in the properties of the n...

The System of Vector Variational-like Inequalities with Weakly Relaxed ${eta_gamma-alpha_gamma}_{gamma inGamma}$ Pseudomonotone Mappings in Banach Spaces

In this paper, we introduce two concepts of weakly relaxed ${eta_gamma-alpha_gamma}_{gamma in Gamma}$ pseudomonotone and demipseudomonotone mappings in Banach spaces. Then we obtain some results of the solutions existence for a system of vector variational-like inequalities with weakly relaxed ${eta_gamma-alpha_gamma}_{gamma in Gamma}$ pseudomonotone and demipseudomonotone mappings in reflexive...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

The Complete Continuity Property in Banach Spaces

Let X be a complex Banach space. We show that the following are equivalent: (i) X has the complete continuity property, (ii) for every (or equivalently for some) 1 < p < ∞, for f ∈ h(D, X) and rn ↑ 1, the sequence frn is p-Pettis-Cauchy, where frn is defined by frn(t) = f(rne ) for t ∈ [0, 2π], (iii) for every (or equivalently for some) 1 < p < ∞, for every μ ∈ V (X), the bounded linear operato...