COPIES OF c0(Γ) IN C(K,X) SPACES
نویسنده
چکیده
We extend some results of Rosenthal, Cembranos, Freniche, E. Saab-P. Saab and Ryan to study the geometry of copies and complemented copies of c0(Γ) in the classical Banach spaces C(K,X) in terms of the cardinality of the set Γ, of the density and caliber of K and of the geometry of X and its dual space X∗. Here are two sample consequences of our results: (1) If C([0, 1], X) contains a copy of c0(א1), then X contains a copy of c0(א1). (2) C(βN, X) contains a complemented copy of c0(א1) if and only if X contains a copy of c0(א1). Some of our results depend on set-theoretic assumptions. For example, we prove that it is relatively consistent with ZFC that if C(K) contains a copy of c0(א1) and X has dimension א1, then C(K,X) contains a complemented copy of c0(א1).
منابع مشابه
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