A NOTE ON CERTAIN QUOTIENT SPACES OF BOUNDED LINEAR OPERATORS
Copyright policy )A NOTE ON CERTAIN QUOTIENT SPACES OF BOUNDED LINEAR OPERATORS
Summary: Suppose \(X\) is a closed subspace of \(Z=(\sum_{n=1}^\infty Z_n)_p\) \((1 <\infty,\;\dim Z_n < \infty)\). We investigate an isometrically isomorphic embedding of \(L(X)/K(X)\) into \(L(X,Z)/K(X,Z)\), where \(L(X,Z)\) (resp. \(L(X)\)) is the space of the bounded linear operators from \(X\) to \(Z\) (resp. from \(X\) to \(X\)) and \(K(X,Z)\) (resp. \(K(X)\)) is the space of the compact linear operators from \(X\) to \(Z\) (resp. from \(X\) to \(X\)).
Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Isometric theory of Banach spaces, Linear spaces of operators, Spaces of operators; tensor products; approximation properties
Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Isometric theory of Banach spaces, Linear spaces of operators, Spaces of operators; tensor products; approximation properties
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