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.
M(r, s)-ideal and M-ideal of compact operators property M*(r, s) compact approximation property
46B20 46B04 46B28 47L05
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