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M(r, s)-ideals of compact operators

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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.

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Authors and Affiliations

  1. Institute of Mathematics, University of Tartu, J. Liivi 2, 50409, Tartu, Estonia

    Rainis Haller, Marje Johanson & Eve Oja

  2. Estonian Academy of Sciences, Kohtu 6, 10130, Tallinn, Estonia

    Eve Oja

Authors
  1. Rainis Haller
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  2. Marje Johanson
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  3. Eve Oja
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Correspondence to Rainis Haller.

Additional information

The research was supported in part by Estonian Science Foundation Grants 7308 and 8976 and Estonian Targeted Financing Project SF0180039s08.

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Haller, R., Johanson, M. & Oja, E. M(r, s)-ideals of compact operators. Czech Math J 62, 673–693 (2012). https://doi.org/10.1007/s10587-012-0059-9

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