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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Sums and products of Hilbert spaces


Author: Jesús M. F. Castillo
Journal: Proc. Amer. Math. Soc. 105 (1989), 362-366
MSC: Primary 46A05; Secondary 46C99, 46M05
DOI: https://doi.org/10.1090/S0002-9939-1989-99953-3
Later version: Proc. Amer. Math. Soc. 107, no. 1 (1974), 101-105
MathSciNet review: 935103
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Abstract: Let $ H$ be a Hilbert space. We prove that the locally convex sum $ { \oplus _I}H$ is a subspace of the product $ {H^J}$ if and only if $ I$ is countable, $ H$ is infinite dimensional, and card $ J \geq {2^{{\aleph _0}}}$.


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DOI: https://doi.org/10.1090/S0002-9939-1989-99953-3
Article copyright: © Copyright 1989 American Mathematical Society

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