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M(r, s)-ideals of compact operators

Research paper by Rainis Haller, Marje Johanson, Eve Oja

Indexed on: 18 Oct '12Published on: 18 Oct '12Published in: Czechoslovak Mathematical Journal



Abstract

We study the position of compact operators in the space of all continuous linear operators and its subspaces in terms of ideals. One of our main results states that for Banach spaces X and Y the subspace of all compact operators K (X, Y) is an M(r1r2, s1s2)-ideal in the space of all continuous linear operators L(X, Y) whenever K (X,X) and K (Y, Y) are M(r1, s1)- and M(r2, s2)-ideals in L(X,X) and L(Y, Y), respectively, with r1 + s1/2 > 1 and r2 +s2/2 > 1. We also prove that the M(r, s)-ideal K (X, Y ) in L(X, Y ) is separably determined. Among others, our results complete and improve some well-known results on M-ideals.