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Strategically reproducible bases and the factorization property

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Abstract

We introduce the concept of strategically reproducible bases in Banach spaces and show that operators which have large diagonal with respect to strategically reproducible bases are factors of the identity. We give several examples of classical Banach spaces in which the Haar system is strategically reproducible: multi-parameter Lebesgue spaces, mixed-norm Hardy spaces and most significantly the space L1. Moreover, we show the strategical reproducibility is inherited by unconditional sums.

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Authors and Affiliations

  1. Institute of Analysis, Johannes Kepler University Linz, Altenberger Strasse 69, A-4040, Linz, Austria

    Richard Lechner & Paul F. X. Müller

  2. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Pavlos Motakis

  3. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA

    Thomas Schlumprecht

  4. Faculty of Electrical Engineering, Czech Technical University in Prague, Technika 2, 16627, Praha 6, Czech Republic

    Thomas Schlumprecht

Authors
  1. Richard Lechner
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  2. Pavlos Motakis
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  3. Paul F. X. Müller
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  4. Thomas Schlumprecht
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Corresponding author

Correspondence to Thomas Schlumprecht.

Additional information

The first and the third author were supported by the Austrian Science Foundation (FWF) under Grant Number Pr. Nr. P28352.

The second-named author was supported by the National Science Foundation under Grant Numbers DMS-1600600 and DMS-1912897.

The fourth-named author was supported by the National Science Foundation under Grant Numbers DMS-1464713 and DMS-1711076.

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Lechner, R., Motakis, P., Müller, P.F.X. et al. Strategically reproducible bases and the factorization property. Isr. J. Math. 238, 13–60 (2020). https://doi.org/10.1007/s11856-020-2011-2

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  • DOI: https://doi.org/10.1007/s11856-020-2011-2

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