• Paul R. Halmos
Part of the Graduate Texts in Mathematics book series (GTM, volume 19)


If M and N are orthogonal subspaces of a Hilbert space, then M + N is closed (and therefore M + N = MN). Orthogonality may be too strong an assumption, but it is sufficient to ensure the conclusion. It is known that something is necessary; if no additional assumptions are made, then M + N need not be closed (see [50, p. 28], and Problems 52–55 below). Here is the conclusion under another very strong but frequently usable additional assumption.


Hilbert Space Cardinal Number Linear Manifold Infinite Dimension Elegant Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag New York Inc. 1982

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  • Paul R. Halmos

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