Strict quasicomplements and the operators of dense imbedding
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A quasicomplementM to a subspaceN of a Banach spaceX is called strict ifM does not contain an infinite-dimensional subspaceM 1 such that the linear manifoldN+M 1 is closed. It is proved that ifX is separable, thenN always admits a strict quasicomplement. We study the properties of the restrictions of the operators of dense imbedding to infinite-dimensional closed subspaces of a space where these operators are defined.
KeywordsHilbert Space Banach Space Compact Operator Linear Span Separable Banach Space
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