Characterization on fuzzy soft ordered Banach algebra. (English) Zbl 07801926
Summary: 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 character is isomorphism to the set of all maximal fuzzy soft algebra cone. We prove that the set of all real \(FS^x\)-characters is convex and extreme point, we applied Gelfand-Mazur theorem on fuzzy soft Banach algebra, we showed that \(FS^x\)-character (the set of all complex continuous \(FS^x\)-character) is fuzzy soft ordered Banach algebra. Also, any \(FS^x\)-OBA with inverse-closed \(FS^x\)-algebra cone \(\breve{C} \) and a non-zero element in \(\breve{A}\) has inverse we have it is an isomorphism to Banach space \(Ch (\breve{C})\).
MSC:
| 46S40 | Fuzzy functional analysis |
| 46J10 | Banach algebras of continuous functions, function algebras |
Keywords:
fuzzy soft sets; fuzzy soft algebra cone; fuzzy soft ordered Banach algebra; maximal fuzzy soft ordered Banach algebra; fuzzy soft Banach algebraReferences:
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