Some Remarks on Countably Determined Measures and Uniform Distribution of Sequences.
A new class of weakly -analytic Banach spaces
In this paper we define and investigate a new subclass of those Banach spaces which are -analytic in their weak topology; we call them strongly weakly -analytic (SWKA) Banach spaces. The class of SWKA Banach spaces extends the known class of strongly weakly compactly generated (SWCG) Banach spaces (and their subspaces) and it is related to that in the same way as the familiar classes of weakly -analytic (WKA) and weakly compactly generated (WCG) Banach spaces are related. We show that: (i) not...
A note on the structure of WUR Banach spaces
We present an example of a Banach space admitting an equivalent weakly uniformly rotund norm and such that there is no , for any set , linear, one-to-one and bounded. This answers a problem posed by Fabian, Godefroy, Hájek and Zizler. The space is actually the dual space of a space which is a subspace of a WCG space.
Equilateral sets in Banach spaces of the form C(K)
We show that for "most" compact nonmetrizable spaces, the unit ball of the Banach space C(K) contains an uncountable 2-equilateral set. We also give examples of compact nonmetrizable spaces K such that the minimum cardinality of a maximal equilateral set in C(K) is countable.
Corrigendum to ``Isometric embeddings of a class of separable metric spaces into Banach spaces''
Isometric embeddings of a class of separable metric spaces into Banach spaces
Let be a bounded countable metric space and a constant, such that , for any pairwise distinct points of . For such metric spaces we prove that they can be isometrically embedded into any Banach space containing an isomorphic copy of .
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