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Proceedings of the American Mathematical Society
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. 107 (1989), 101-105
MSC: Primary 46A05; Secondary 46C99, 46M05
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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^{{\chi _0}}}$.


References [Enhancements On Off] (What's this?)

  • [1] Hans Jarchow, Locally convex spaces, B. G. Teubner, Stuttgart, 1981. Mathematische Leitfäden. [Mathematical Textbooks]. MR 632257 (83h:46008)
  • [2] Gottfried Köthe, Topological vector spaces. I, Translated from the German by D. J. H. Garling. Die Grundlehren der mathematischen Wissenschaften, Band 159, Springer-Verlag New York Inc., New York, 1969. MR 0248498 (40 #1750)
  • [3] Gottfried Köthe, Topological vector spaces. II, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 237, Springer-Verlag, New York-Berlin, 1979. MR 551623 (81g:46001)
  • [4] Jesús M. F. Castillo, The sum problem for Hilbert spaces, Extracta Math. 3 (1) (1988), 26-27.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-89-99996-6
PII: S 0002-9939(89)99996-6
Article copyright: © Copyright 1989 American Mathematical Society