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Polynomial versions of weak Dunford–Pettis properties in Banach lattices

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Abstract

In this paper, we introduce polynomial versions of the weak Dunford–Pettis property and the weak Dunford–Pettis\(^{*}\) property for Banach lattices. By using Fremlin projective Banach lattice tensor products, we obtain several characterizations of the weak Dunford–Pettis property and the weak Dunford–Pettis\(^{*}\) property in terms of regular homogeneous polynomials on Banach lattices.

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Authors and Affiliations

  1. Department of Mathematics, North China University of Water Resources and Electric Power, Zhengzhou, 450045, Henan, China

    Yu Wang

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Zhongrui Shi

  3. Department of Mathematics, University of Mississippi, University, MS, 38677, USA

    Qingying Bu

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  1. Yu Wang
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  2. Zhongrui Shi
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  3. Qingying Bu
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Correspondence to Qingying Bu.

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This research is supported by NNSF of China (Grant Nos. 11771273, 11971493).

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Wang, Y., Shi, Z. & Bu, Q. Polynomial versions of weak Dunford–Pettis properties in Banach lattices. Positivity 25, 1685–1698 (2021). https://doi.org/10.1007/s11117-021-00837-2

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