• A note on generalized characters

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/115/04/0437-0444

    • Keywords

       

      Compactly generated LCA group; character; generalized character; Gel’fand space; commutative topological algebra

    • Abstract

       

      For a compactly generated LCA group G, it is shown that the setH(G) of all generalized characters on G equipped with the compact-open topology is a LCA group andH(G) = Ĝ (the dual group ofG) if and only ifG is compact. Both results fail for arbitrary LCA groups. Further, ifG is second countable, then the Gel’fand space of the commutative convolution algebraCc(G) equipped with the inductive limit topology is topologically homeomorphic toH(G).

    • Author Affiliations

       

      S J Bhatt1 H V Dedania1

      1. Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar - 388 120, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.