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Czechoslovak Mathematical Journal

, Volume 62, Issue 3, pp 673–693 | Cite as

M(r, s)-ideals of compact operators

  • Rainis Haller
  • Marje Johanson
  • Eve Oja
Article

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(r 1 r 2, s 1 s 2)-ideal in the space of all continuous linear operators L(X, Y) whenever K (X,X) and K (Y, Y) are M(r 1, s 1)- and M(r 2, s 2)-ideals in L(X,X) and L(Y, Y), respectively, with r 1 + s 1/2 > 1 and r 2 +s 2/2 > 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.

Keywords

M(r, s)-ideal and M-ideal of compact operators property M*(r, scompact approximation property 

MSC 2010

46B20 46B04 46B28 47L05 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2012

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of TartuTartuEstonia
  2. 2.Estonian Academy of SciencesTallinnEstonia

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