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

Abstract : 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 $K,L,M,N$.
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https://hal.archives-ouvertes.fr/hal-03190904
Contributor : Christian Samuel <>
Submitted on : Tuesday, April 6, 2021 - 5:30:18 PM
Last modification on : Wednesday, April 7, 2021 - 3:29:25 AM

### Identifiers

• HAL Id : hal-03190904, version 1
• ARXIV : 2012.13439

### Citation

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

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