New Results of Characterization on Symmetric Ordered S-Banach Algebra

Abstract

This paper investigates the character of symmetric S-ordered Banach algebra with identity. First, we introduce the concepts of s-norm and quasi-s-norm and then define the symmetric ordered Banach algebra (SOBA) with Symmetric algebra cone C. We introduce the concept of S-character on (SOBA) and show that the set of all S-characters is compact, continuous, and has the s-norm, as well as being hermitian functional and proving new results.