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Proceedings of the American Mathematical Society

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Subspace of $ {\rm LC}(H)$ and $ C\sb{p}$


Author: Yaakov Friedman
Journal: Proc. Amer. Math. Soc. 53 (1975), 117-122
MSC: Primary 47D15; Secondary 47B10
MathSciNet review: 0377592
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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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DOI: https://doi.org/10.1090/S0002-9939-1975-0377592-X
Keywords: Hilbert spaces, $ {C_p}$ spaces, $ {l_p}$ spaces, orthogonal projection, complemented subspaces
Article copyright: © Copyright 1975 American Mathematical Society