Abstract
Abstract
Galego and Samuel showed that if K, L are metrizable, compact, Hausdorff spaces, then
$C(K)\widehat{\otimes}_\pi C(L)$
is c0-saturated if and only if it is subprojective if and only if K and L are both scattered. We remove the hypothesis of metrizability from their result and extend it from the case of the twofold projective tensor product to the general n-fold projective tensor product to show that for any
$n\in\mathbb{N}$
and compact, Hausdorff spaces K1, …, K
n
,
$\widehat{\otimes}_{\pi, i=1}^n C(K_i)$
is c0-saturated if and only if it is subprojective if and only if each K
i
is scattered.
Publisher
Cambridge University Press (CUP)
Reference17 articles.
1. Spaces of continuous functions (III) (Spaces C(Ω) for Ω without perfect subsets)
2. 16. Samuel, C. , Indice de Szlenk des C(K), Séeminaire de Géométrie des espaces de Banach, Vol. I-II, Publications Mathématiques de l’Universitée Paris VII, Paris (1983) 81–91.
3. 5. Causey, R. M. , Galego, E. and Samuel, C. , The Szlenk index of $C(K)\widehat{\otimes}_\pi C(L)$ , preprint.
4. Reflexivity in Banach lattices
5. Szlenk and w⁎-dentability indices of C(K)