Multiplicative and almost multiplicative maps in probabilistic normed algebras

	Multiplicative and almost multiplicative maps in probabilistic normed algebras
International Journal of Nonlinear Analysis and Applications
مقاله 8، دوره 14، شماره 6، شهریور 2023، صفحه 99-108 اصل مقاله (393.41 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.26345.3298
نویسنده
Hamid Shayanpour^*
Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 88186-34141, Shahrekord, Iran
چکیده
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.
کلیدواژه‌ها
Multiplicative map؛ almost multiplicative map؛ probabilistic normed algebras
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