International Journal of Nonlinear Analysis and Applications

Multiplicative and almost multiplicative maps in probabilistic normed algebras

Document Type : Research Paper

Author

Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 88186-34141, Shahrekord, Iran

Abstract

Our main purpose of this paper is to study the relationship between multiplicative maps and almost multiplicative maps between probabilistic normed algebras. We first derive some properties of invertible elements and their relation with multiplicative maps. Then we show that every complex homomorphism on elements whose probabilistic norm is equal to 1, is bounded. In the following, we give an open problem about the functionally continuous of unital commutative probabilistic Banach algebra. Finally, we prove that every almost multiplicative map that is not a multiplicative map is continuous.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 6
June 2023
Pages 99-108
  • Receive Date: 18 February 2022
  • Revise Date: 08 May 2022
  • Accept Date: 21 May 2022