Using the technique of Fraïssé theory, for every constant , we construct a universal object in the class of Banach spaces possessing a normalized -suppression unconditional Schauder basis.
This paper is an investigation of the universal separable metric space up to isometry U discovered by Urysohn. A concrete construction of U as a metric subspace of the space C[0,1] of functions from [0,1] to the reals with the supremum metric is given. An answer is given to a question of Sierpiński on isometric embeddings of U in C[0,1]. It is shown that the closed linear span of an isometric copy of U in a Banach space which contains the zero of the Banach space is determined up to linear isometry....
We consider biorthogonal systems of functions on the interval [0,1] or 𝕋 which have the same dyadic scaled estimates as wavelets. We present properties and examples of these systems.
We characterize Banach lattices on which every positive almost Dunford-Pettis operator is weakly compact.
For Banach spaces and , let denote the space of all continuous compact operators from to endowed with the operator norm. A Banach space has the property if every Grothendieck subset of is relatively weakly compact. In this paper we study Banach spaces with property . We investigate whether the spaces and have the property, when and have the property.
Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.
Sufficient conditions are given in order that, for a bounded closed convex subset of a locally convex space , the set of continuous functions from the compact space into , is the uniformly closed convex hull in of its extreme points. Applications are made to the unit ball of bounded (or compact, or weakly compact) operators from certain Banach spaces into .