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Linear L–Positive Sets and Their Polar Subspaces

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Abstract

In this paper, we define a Banach SNL space to be a Banach space with a certain kind of linear map from it into its dual, and we develop the theory of linear L–positive subsets of Banach SNL spaces with Banach SNL dual spaces. We use this theory to give simplified proofs of some recent results of Bauschke, Borwein, Wang and Yao, and also of the classical Brezis–Browder theorem.

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  1. Department of Mathematics, University of California, Santa Barbara, CA, 93106-3080, USA

    S. Simons

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  1. S. Simons
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Correspondence to S. Simons.

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Simons, S. Linear L–Positive Sets and Their Polar Subspaces. Set-Valued Var. Anal 20, 603–615 (2012). https://doi.org/10.1007/s11228-012-0206-3

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  • DOI: https://doi.org/10.1007/s11228-012-0206-3

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