• A note on generalized characters

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    • 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

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