Hereditary D-property of function spaces over compacta

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

A new class of function spaces on domains of R^d and its relations to classical function spaces

Ju n 20 07 Spaces of continuous functions over Dugundji compacta

We show that for every Dugundji compact K of weight א1 the Banach space C(K) is 1Plichko and the space P (K) of probability measures onK is Valdivia compact. Combining this result with the existence of a non-Valdivia compact group, we answer a question of Kalenda. 2000Mathematics Subject Classification. Primary: 46B26; Secondary: 46E15, 54C35, 54D30.

Topological properties of the continuous function spaces on some ordered compacta

Some new classes of compacta K are considered for which C(K) endowed with the pointwise topology has a countable cover by sets of small local norm–diameter.

Hereditary Approximation Property

If X is a Banach space such that the isomorphism constant to `2 from n dimensional subspaces grows sufficiently slowly as n → ∞, then X has the approximation property. A consequence of this is that there is a Banach space X with a symmetric basis but not isomorphic to `2 so that all subspaces of X have the approximation property. This answers a problem raised in 1980 [8]. An application of the ...