Subspace of 𝐿𝐶(𝐻) and 𝐶_{𝑝}

Friedman, Yaakov

doi:10.1090/S0002-9939-1975-0377592-X

Subspace of $\textrm {LC}(H)$ and $C_{p}$
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by Yaakov Friedman PDF

Proc. Amer. Math. Soc. 53 (1975), 117-122 Request permission

Abstract:

This paper deals with certain properties of the subspaces of $LC(H)$ and ${C_p}$ and namely those connected with the reflexivity and with the property of containing classical spaces. It is proved that any subspace of ${C_p}(1 \leqslant p < \infty )$ is either isomorphic to Hilbert space or it contains a subspace isomorphic to ${l_p}$. For ${C_1}$ and $LC(H)$ the same results were obtained by J. R. Holub, cf. [4].

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