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Subsymmetric weak$^*$ Schauder bases and factorization of the identity

Volume 248 / 2019

Richard Lechner Studia Mathematica 248 (2019), 295-319 MSC: 46B25, 46B26. DOI: 10.4064/sm180404-29-9 Published online: 22 March 2019

Abstract

We provide conditions on a dual Banach space $X^*$ with a subsymmetric weak$^*$ Schauder basis which allow us to ensure that for any bounded operator $T \colon X^*\to X^*$, either $T(X^*)$ or $({\rm Id}_{X^*}-T)(X^*)$ contains a subspace that is isomorphic to $X^*$ and complemented in $X^*$. Under the same conditions on $X^*$, we prove that $\ell ^p(X^*)$, $1\leq p \leq \infty $, is primary. Moreover, we show that these conditions are satisfied by a wide range of Orlicz and Lorentz sequence spaces.

Authors

  • Richard LechnerInstitute of Analysis
    Johannes Kepler University Linz
    Altenberger Straße 69
    A-4040 Linz, Austria
    e-mail

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