Asplund spaces
Folner's Conditions for Amenable Semi-Groups.
Complements of sets of unstable points
On certain actions of semi-groups on L-spaces
Intersection Numbers and Weak* Separability of Spaces of Measures.
The Lindelöf property and σ-fragmentability
In the previous paper, we, together with J. Orihuela, showed that a compact subset X of the product space is fragmented by the uniform metric if and only if X is Lindelöf with respect to the topology γ(D) of uniform convergence on countable subsets of D. In the present paper we generalize the previous result to the case where X is K-analytic. Stated more precisely, a K-analytic subspace X of is σ-fragmented by the uniform metric if and only if (X,γ(D)) is Lindelöf, and if this is the case then...
σ-fragmented Banach spaces II
Recent papers have investigated the properties of σ-fragmented Banach spaces and have sought to find which Banach spaces are σ-fragmented and which are not. Banach spaces that have a norming M-basis are shown to be σ-fragmented using weakly closed sets. Zizler has shown that Banach spaces satisfying certain conditions have locally uniformly convex norms. Banach spaces that satisfy similar, but weaker conditions are shown to be σ-fragmented. An example, due to R. Pol, is given of a Banach space that...
Fragmentability and σ-fragmentability
Recent work has studied the fragmentability and σ-fragmentability properties of Banach spaces. Here examples are given that justify the definitions that have been used. The fragmentability and σ-fragmentability properties of the spaces and , with Γ uncountable, are determined.
The Lindelöf property in Banach spaces
A topological space (T,τ) is said to be fragmented by a metric d on T if each non-empty subset of T has non-empty relatively open subsets of arbitrarily small d-diameter. The basic theorem of the present paper is the following. Let (M,ϱ) be a metric space with ϱ bounded and let D be an arbitrary index set. Then for a compact subset K of the product space the following four conditions are equivalent: (i) K is fragmented by , where, for each S ⊂ D, . (ii) For each countable subset A of D, is...
Norm fragmented weak* compact sets.
A Banach space which is a Cech-analytic space in its weak topology has fourteen measure-theoretic, geometric and topological properties. In a dual Banach space with its weak-star topology essentially the same properties are all equivalent one to another.
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