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- W1503619663 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 cardinality 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 $c_0(aleph _1)$, then $X$ contains a copy of $c_0(aleph _1)$. [(2)] $C(beta mathbb N,X)$ contains a complemented copy of $c_{0}(aleph _{1})$ if and only if $X$ contains a copy of $c_{0}(aleph _{1})$. 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 $c_0(aleph _1)$ and $X$ has dimension $aleph _1$, then $C(K,X)$ contains a complemented copy of $c_0(aleph _1)$." @default.
- W1503619663 created "2016-06-24" @default.
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- W1503619663 date "2012-11-01" @default.
- W1503619663 modified "2023-10-16" @default.
- W1503619663 title "Copies of $c_{0}(Γ)$ in $C(K, X)$ spaces" @default.
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- W1503619663 doi "https://doi.org/10.1090/s0002-9939-2012-11208-0" @default.
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