A NOTE ON CERTAIN QUOTIENT SPACES OF BOUNDED LINEAR OPERATORS

Title & Authors
A NOTE ON CERTAIN QUOTIENT SPACES OF BOUNDED LINEAR OPERATORS
Cho, Chong-Man; Ju, Seong-Jin;

Abstract
Suppose X is a closed subspace of Z = $\small{{({{\Sigma}^{\infty}}_{n=1}Z_{n})}_{p}}$ (1 < p < $\small{{\infty}}$, dim $\small{Z_{n}}$ < $\small{{\infty}}$). 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).
Keywords
bounded linear operator;compact operator;quotient space;$\small{{\ell}_p}$-sum;
Language
English
Cited by
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