• Two results on strong proximinality

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      https://www.ias.ac.in/article/fulltext/pmsc/131/0015

    • Keywords

       

      Proximinal subspaces; strongly proximinal subspaces; strong subdifferentiability.

    • Abstract

       

      Let $Y \subseteq X$ be a closed subspace. By a simple argument, we show that $Y^{\bot\bot} X^{**}$ is strongly proximinal at points of $X$ if and only if $Y$ is a strongly proximinal subspace of $X$. This substantially improves the main result of Jayanarayanan and Paul (J. Math. Anal. Appl. 426 (2015) 1217--1231). As a consequence we get an easy proof of a classical result of Alfsen and Effros (Ann. Math. 98 (1972) 98--173), that $M$-ideals are proximinal subspaces and a result of Dutta and Narayana (Function Spaces,Contemporary Mathematics, vol. 435, American Mathematical Society, Providence(2007) pp. 143--152), that $M$-ideals are strongly proximinal subspaces.

    • Author Affiliations

       

      T S S R K Rao1

      1. Department of Mathematics, Ashoka University, Rajiv Gandhi Education City, Sonipat 131 029, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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