10.30495/maca.2022.1955532.1055

On various properties of module Lau product of algebras

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  • Prakash A. Dabhi1,
  • Yuvraj D. Pipaliya2,
  1. Department of Mathematics, Institute of Infrastructure Technology Research and Management (IITRAM), Ahmedabad-380026, Gujarat, India
  2. Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar-388120, Gujarat, India; General Department, Government Polytechnic, Junagadh-362263, Gujarat, India

Published in Issue 2022-09-23

How to Cite

On various properties of module Lau product of algebras. (2022). Mathematical Analysis and Its Contemporary Applications, 4(4). https://doi.org/10.30495/maca.2022.1955532.1055

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Abstract

Let A, B, and X be complex algebras, θ : B -> X be an algebra homomorphism, and let A be an X-bimodule. We define a product on A × B as (a1, b1)(a2, b2) = (a1a2 + a1 · θ(b2) + θ(b1) ◦ a2, b1b2) for all (a1, b1), (a2, b2) ∈ A × B and write A × B with this product by A ×θ B. We shall study some basic properties of A ×θ B. When A, B and X are Banach algebras, A is a Banach X-bimodule, and θ is a continuous homomorphism with the norm at most 1, we determine the ideals of A ×θ B of a certain type, the Gelfand space of this Banach algebra, and the module multipliers of this Banach algebra.

Keywords

  • Module Lau-product of Banach algebras,
  • ideals,
  • Gelfand space,
  • module multipliers
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References

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