Common complements of two subspaces of a Hilbert space |
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Authors: | Michael Lauzon |
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Affiliation: | Department of Mathematics, Brown University, PO Box 1917, Providence, RI 02912, USA |
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Abstract: | In this paper we find a necessary and sufficient condition for two closed subspaces, and , of a Hilbert space to have a common complement, i.e. a subspace having trivial intersection with and and such that .Unlike the finite-dimensional case the condition is significantly more subtle than simple equalities of dimensions and codimensions, and non-trivial examples of subspaces without a common complement are possible. |
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Keywords: | Common complement Complementary subspaces Hilbert space geometry Gramian Lower linear dimension Upper linear codimension |
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