Sums and products of Hilbert spaces
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- by Jesús M. F. Castillo PDF
- Proc. Amer. Math. Soc. 107 (1989), 101-105 Request permission
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
- Hans Jarchow, Locally convex spaces, Mathematische Leitfäden. [Mathematical Textbooks], B. G. Teubner, Stuttgart, 1981. MR 632257
- Gottfried Köthe, Topological vector spaces. I, Die Grundlehren der mathematischen Wissenschaften, Band 159, Springer-Verlag New York, Inc., New York, 1969. Translated from the German by D. J. H. Garling. MR 0248498
- Gottfried Köthe, Topological vector spaces. II, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 237, Springer-Verlag, New York-Berlin, 1979. MR 551623 Jesús M. F. Castillo, The sum problem for Hilbert spaces, Extracta Math. 3 (1) (1988), 26-27.
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 101-105
- MSC: Primary 46A05; Secondary 46C99, 46M05
- DOI: https://doi.org/10.1090/S0002-9939-89-99996-6