Points of Weak-Norm Continuity in the Unit Ball of Banach Spaces

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...

On fixed points of fundamentally nonexpansive mappings in Banach spaces

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

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...

Weighted Composition Operators between Mixed Norm Spaces and H ∞ α Spaces in the Unit Ball

On the Proximinality of the Unit Ball of Proximinal Subspaces in Banach Spaces: a Counterexample

A known, and easy to establish, fact in Best Approximation Theory is that, if the unit ball of a subspace G of a Banach space X is proximinal in X, then G itself is proximinal in X. We are concerned in this article with the reverse implication, as the knowledge of whether the unit ball is proximinal or not is useful in obtaining information about other problems. We show, by constructing a count...