On (a, B, c)-ideals in Banach spaces

  • Ksenia Niglas Faculty of Mathematics and Computer Science, Tartu University, J. Liivi 2, 50409 Tartu
  • Indrek Zolk Faculty of Mathematics and Computer Science, Tartu University, J. Liivi 2, 50409 Tartu
Keywords: Banach spaces, (a, B, c)-ideals

Abstract

In this paper we focus on subspaces of Banach spaces that are (a, B, c)-ideals. We study (a, B, c)-ideals in l2 and present easily verifiable conditions for a subspace of l2 to be an (a, B, c)-ideal. Our main results concern the transitivity of (a, B, c)-ideals. We show that if X is an (a, B, c)-ideal in Y and Y is a (d, E, f)-ideal in Z, then X is a certain type of ideal in Z. Relying on this result, we show that if X is an (a, B, c)-ideal in its bidual, then X is a certain type of ideal in X(2n) for every n ∈ N.

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Published
2014-06-25
Section
Articles