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N Subspaces

Published online by Cambridge University Press:  20 November 2018

V. S. Sunder
V. S. Sunder*
Affiliation:
Indian Statistical Institute, New Delhi, India
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It is a well-known fact (cf., for instance Lemma 7.3.1 of [8], and also [2] and [4] ) that if M and N are closed subspaces of a finite-dimensional Hilbert space, and if M and N are in ‘generic’ position (i.e., any two of the four subspaces M, M⊥ , N, N⊥ have trivial intersection), then N is the graph of a linear isomorphism of M onto M⊥ . To be sure, there exist infinite-dimensional versions of this, where one must allow for unbounded operators in case the ‘gap’ between M and N is zero, in the sense of Kato [7]. (There is an extensive literature on pairs of subspaces, [2], [3], [4], [6] and [7], to cite a few; for a fairly extensive bibliography, see [3].)

This paper addresses itself to the case of n (2 ≦ n< ∞) subspaces.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 1 , 01 February 1988, pp. 38 - 54
Copyright
Copyright © Canadian Mathematical Society 1988

References

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