Orthogonality and linear mappings in Banach modules over a unital C∗-algebra – Moroccan Journal of Algebra and Geometry with Applications

Moroccan Journal of Algebra and Geometry with Applications

Orthogonality and linear mappings in Banach modules over a unital $C^*$ -algebra

Hassan Azadi Kenary
Department of Mathematics, College of Sciences, Yasouj University, Yasouj 75914-353, Iran

Pages 345–357 | Received 26 December 2023, Accepted 18 July 2024, Published 08 November 2024

Abstract

Using the fixed point method, we prove the Hyers-Ulam stability of linear mappings in Banach modules over a unital $C^*$ -algebra and in non-Archimedean Banach modules over a unital $C^*$ -algebra associated with the following orthogonally Cauchy-Jensen additive functional equation.

Keywords: Hyers-Ulam stability, orthogonally Cauchy-Jensen additive functional equation, fixed point, non-Archimedean Banach module over $C^*$ -algebra, orthogonality space.

MSC numbers: 39B55, 46S10, 47H10, 39B52, 47S10, 30G06, 46H25, 46L05, 12J25.

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