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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Subspaces and graphs


Author: Kin Yan Chung
Journal: Proc. Amer. Math. Soc. 119 (1993), 141-146
MSC: Primary 47A05; Secondary 46C99, 46M99, 58B10
MathSciNet review: 1155595
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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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DOI: https://doi.org/10.1090/S0002-9939-1993-1155595-6
Article copyright: © Copyright 1993 American Mathematical Society