Research Paper
Year: 2017 | Month: December | Volume: 4 | Issue: 12 | Pages: 34-42
Isomorphic Classification Sequences of Spaces
Ahmed Yahya M.H1, Muntasir Suhail D.S2
1Department of Mathematics –College of Science & Arts AL Great -Al - Jouf University -Saudi Arabia
Department of Mathematics –College of Science and Technology -University of shendi- Sudan
2Department of Mathematics –College of Science & Arts Oklat Alskoor-Qassim University -Saudi Arabia
Department of Mathematics –College of Science -University of Bakht Er-ruda-Eddwaim- Sudan
Corresponding Author: Ahmed Yahya M.H
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.
Key words: Bessaga-Pełczyński and Milutin’s theorems on separable C(K)spaces Isomorphic classifications of C(K,X) spaces ω_1-quotient of Banach spaces
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