This is an announcement for the paper "Geometry of the Banach spaces C(beta mathbb N times K, l_p) for compact metric spaces K" by Dale E. Alspach and Eloi Medina Galego .
Abstract: In this paper we provide the complete isomorphic classification of the spaces C(beta mathbb N times K, l_p) of all continuous l_p-valued functions, 1 <= p < infinity, defined on the topological product of the Stone-Cech compactification of the natural numbers mathbb N and an arbitrary infinite compact metric space K. In order to do this, we first prove that c_0 is the only infinite dimensional separable C(K) space, Z, up to an isomorphism, which satisfies each one of the following statements: (1) Z is a quotient of C(beta mathbb N, l_p) for every 1< p< infinity. (2) Z is isomorphic to a complemented subspace of C(beta mathbb N, l_1). (3) C(beta mathbb N, l_p) is isomorphic to the injective tensor product of itself and Z, for every 1 <= p < infinity.
Archive classification: math.FA
Mathematics Subject Classification: 46B
Remarks: 17 pages
Submitted from: alspach@math.okstate.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1011.3261
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