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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Complemented subspaces of products of Hilbert spaces

Author: Paweł Domański
Journal: Proc. Amer. Math. Soc. 110 (1990), 187-196
MSC: Primary 46A05; Secondary 46C99
MathSciNet review: 1000152
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Abstract: It is proved that every complemented subspace of an arbitrary topological product of (nonnecessarily separable) Hilbert spaces is isomorphic to a product of Hilbert spaces.

A counterexample is given showing that this result cannot be proved by the same direct method as for countable products.

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Additional Information

PII: S 0002-9939(1990)1000152-2
Keywords: Complemented subspaces, Hilbert spaces, topological products of Hilbert spaces, locally convex spaces
Article copyright: © Copyright 1990 American Mathematical Society