Non-Newtonian approach to C∗− algebras

Abstract

In this article, we study the non-Newtonian version of $C^{\ast }-$algebras. Further, we generalize some results which hold for the classical $C^{\ast }-$algebras. We also discuss some illustrative examples to show accuracy and effectiveness of the new findings. If we take the identity function I instead of the generators α and β in the construction of the set $\mathbb{C}(N),$ then non-Newtonian $C^{\ast }-$algebras turn into the classical $C^{\ast }-$algebras, so our results are stronger than some knowledge and facts in the most existing literature.

Keywords:

• C*– algebra
• homomorphism
• ideal
• non-Newtonian calculus

2020 Mathematics Subject Classification:

• 46L05
• 11U10