Characterization on fuzzy soft ordered Banach algebra

Abstract

In this paper, we define fuzzy soft ordered Banach algebra with fuzzy soft algebra cone, and introduce the character on fuzzy soft ordered Banach algebra in both cases real and complex. Also, we deduce some of its basic properties and we define a new concept which is a maximal fuzzy soft algebra cone and showing that the set of all fuzzy soft character is isomorphism to the set of all maximal fuzzy soft algebra cone. we prove that the set of all real characters is convex and extreme point, we applied Gelfand- Mazur theorem on fuzzy soft Banach algebra, we showed that character (the set of all complex continuous character) is fuzzy soft ordered Banach algebra. with inverse –closed algebra cone ̆ and a non-zero element in ̆ has inverse we have is an isomorphism to Banach space ( ̆)