N Subspaces

  • Sunder V
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Abstract

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.

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APA

Sunder, V. S. (1988). N Subspaces. Canadian Journal of Mathematics, 40(1), 38–54. https://doi.org/10.4153/cjm-1988-002-0

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