Isomorphic Classification Sequences of Spaces
Journal Title: International Journal of Research and Review - Year 2017, Vol 4, Issue 12
Abstract
In this paper we study the isomorphic classifications sequences of C(U_n,X)spaces, the Banach spaces of all continuous X-valued functions defined on infinite compact sequences of metric spacesU_n, equipped with the supremum norm. We first introduce the concept of α+ε -quotient of Banach spaces X. Thus, we prove that if X has some α+ε -quotient which is uniformly convex, then for all U_(n+1)and U_(n+2) the following statements are equivalent: (a) C(U_(n+1),X)is isomorphic to C(U_(n+2),X). (b) C(U_(n+1))is isomorphic to C(U_(n+2)). This allows us to classify, up to an isomorphism, some C(U_n,Y⊕l_p (Γ))spaces, 1 < p ≤∞, and certain C(S_n ) spaces involving large compact Hausdorff sequence spaces S_n.
Authors and Affiliations
Ahmed Yahya M. H
Keywords
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