Countable products of spaces of finite sets
We consider the compact spaces sigma_n(I) of subsets of an uncountable set I of cardinality at most n and their countable products. We give a complete classification of their Banach spaces of continuous functions and a partial topological classification.
On Banach spaces C(K) isomorphic to c₀(Γ)
We give a characterization of compact spaces K such that the Banach spaceC(K) is isomorphic to the spacec0( ) for some set . As an application we show that there exists an Eberlein compact spaceK of weight!! and with the third derived setK (3) empty such that the space C(K) is not isomorphic to any c0( ). For this compactum K, the spaces C(K) and c0(!!) are examples of weakly compactly generated (WCG) Banach spaces which are Lipschitz isomorphic but not isomorphic.
Gâteaux differentiability of convex functions and topology : weak asplund spaces
Canonical Examples of Weak Asplund Spaces. Properties of Gateaux Differentiability Spaces and Weak Asplund Spaces. Stegall's Classes. Two More Concrete Classes of Banach Spaces that Lie in . Fragmentability. "Long Sequences" of Linear Projections. Vasak Spaces and Gul'ko Compacta. A Characterization of WCG Spaces and of Eberlein Compacta. Main Open Questions and Problems. References. Index.