Artículos de revistas
COPIES OF c(0)(Gamma) IN C(K, X) SPACES
Date
2013-08-02Registration in:
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, PROVIDENCE, v. 140, n. 11, supl. 2, Part 2, pp. 3843-3852, NOV, 2012
0002-9939
Author
Galego, Eloi Medina
Hagler, James N.
Institutions
Abstract
We extend some results of Rosenthal, Cembranos, Freniche, E. Saab-P. Saab and Ryan to study the geometry of copies and complemented copies of c(0)(Gamma) in the classical Banach spaces C(K, X) in terms of the carclinality of the set Gamma, 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 c(0)(N-1), then X contains a copy of c(0)(N-1). (2) C(beta N, X) contains a complemented copy of c(0)(N-1) if and only if X contains a copy of c(0)(N-1). 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 c(0)(N-1) and X has dimension NI, then C(K, X) contains a complemented copy of cc(0)(N-1).