• Very smooth points of spaces of operators

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/113/01/0053-0064

    • Keywords

       

      Very smooth points; spaces of operators; M-ideals

    • Abstract

       

      In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is anM-ideal in the space of bounded operators, a very smooth operatorT attains its norm at a unique vectorx (up to a constant multiple) andT(x) is a very smooth point of the range space. We show that if for every equivalent norm on a Banach space, the dual unit ball has a very smooth point then the space has the Radon-Nikodým property. We give an example of a smooth Banach space without any very smooth points.

    • Author Affiliations

       

      T S S R K Rao1

      1. Indian Statistical Institute, R.V. College Post, Bangalore - 560 059, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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