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On the Multiplier Semigroup of a Weighted Abelian Semigroup

Author

Listed:
  • Prakash A. Dabhi

    (Sardar Patel University)

  • Manish Kumar Pandey

    (Sardar Patel University)

Abstract

Let (S, ω) be a weighted abelian semigroup. We show that a ω-bounded semigroup multiplier on S is a multiplication by a bounded function on the space of ω-bounded generalized semicharacters on S; and discuss a converse. Given a ω-bounded multiplier α on S, we investigate the induced weighted semigroup (Sα; ωα). We show that the ωα-bounded generalized semicharacters on Sα are scalar multiples of ω-bounded generalized semicharacters on S. Moreover, if (S0, ω0) is another weighted semigroup formed with some other operation on set S such that ω0-bounded generalized semicharacters on S0 are scalar multiples of ω-bounded generalized semicharacters on S, then it is shown that S0 = Sα under some natural conditions. A number of examples and counter examples are discussed. The paper strengthens the idea that a weighted semigroup provides a semigroup analogue of a normed algebra for which a Gelfand duality may be searched.

Suggested Citation

  • Prakash A. Dabhi & Manish Kumar Pandey, 2019. "On the Multiplier Semigroup of a Weighted Abelian Semigroup," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(1), pages 203-212, March.
    • Handle: RePEc:spr:indpam:v:50:y:2019:i:1:d:10.1007_s13226-019-0318-7
    DOI: 10.1007/s13226-019-0318-7
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