Subspaces and graphs

Chung, Kin Yan

doi:10.1090/S0002-9939-1993-1155595-6

Subspaces and graphs
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Proc. Amer. Math. Soc. 119 (1993), 141-146 Request permission

Abstract:

Subspaces sufficiently near an arbitrary (fixed) subspace of a Hilbert space are shown to be in one-to-one correspondence with operators defined on the given subspace. Specifically, the nearby subspaces can be regarded as the graphs of these operators. This is applied to explicitly define a ${C^\infty }$-atlas of charts for the set of subspaces.

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