On the Multiplier Semigroup of a Weighted Abelian Semigroup

Prakash A. Dabhi () and Manish Kumar Pandey ()
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Prakash A. Dabhi: Sardar Patel University
Manish Kumar Pandey: Sardar Patel University

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 1, 203-212

Abstract: 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.

Keywords: Multipliers on commutative Banach algebra; weighted semigroup; multipliers on a semigroup (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0318-7

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