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Pré-Publication, Document De Travail Année : 2021

Szlenk index of $C(K)\widehat{\otimes}_\pi C(L)$

R. M. Causey
  • Fonction : Auteur
E. Galego
  • Fonction : Auteur

Résumé

We compute the Szlenk index of an arbitrary projective tensor product $C(K)\widehat{\otimes}_\pi C(L)$ of spaces $C(K), C(L)$ of continuous functions on scattered, compact, Hausdorff spaces. In particular, we show that it is simply equal to the maximum of the Szlenk indices of the spaces $C(K), C(L)$. We deduce several results regarding non-isomorphism of $C(K)\widehat{\otimes}_\pi C(L)$ and $C(M)$ or $C(M)\widehat{\otimes}_\pi C(N)$ for particular choices of $K,L,M,N$.

Dates et versions

hal-03190904 , version 1 (06-04-2021)

Identifiants

Citer

R. M. Causey, E. Galego, Christian Samuel. Szlenk index of $C(K)\widehat{\otimes}_\pi C(L)$. 2021. ⟨hal-03190904⟩
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