Isometries of certain operator spaces

Khalil, R.; Saleh, A.

doi:10.1090/S0002-9939-03-07210-1

Isometries of certain operator spaces
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by R. Khalil and A. Saleh PDF

Proc. Amer. Math. Soc. 132 (2004), 1473-1481 Request permission

Abstract:

Let $X$ and $Y$ be Banach spaces, and $L(X,Y)$ be the spaces of bounded linear operators from $X$ into $Y.$ In this paper we give full characterization of isometric onto operators of $L(X,Y),$ for a certain class of Banach spaces, that includes $\ell ^{p},$ $1<p<\infty .$ We also characterize the isometric onto operators of $L(c_{0})$ and $K(\ell ^{1}),$ the compact operators on $\ell ^{1}.$ Furthermore, the multiplicative isometric onto operators of $L(\ell ^{1})$, when multiplication on $L(\ell ^{1})$ is taken to be the Schur product, are characterized.

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