چکیده

C^ * Algebra is a special type of Banach algebra which is a generalization of complex numbers in C^ * algebra concepts such as positive elements inequalities and the like are defined based on properties but a Banach algebra does not have the properties of C^ * algebra. Some examples of Banach algebras like L^1 are not an C^ * algebra. Now we want concepts such as positive elements inequalities and the like to be defined in Banach algebras without relying on C^ * algebra properties and these concepts are defined based on the characteristics of Banach algebra characters therefore many of the results in C^ * algebras can be generalized to Banach algebras. This article generalizes the definition of positive elements from C^ * algebra to Banach algebra. Positive elements are defined based on characters (Multiplicative linear functional) Which contains almost all the properties of positive elements of C^ * algebras and most theorems are proved by this definition. By defining the inequalities in Banach algebra and studing the properties of the inequalities valid results can be obtained.

کليدواژه ها

Hermitian element Banach subalgebra Hereditary Approximate Identity

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, 1401 , Generalization of some properties of C^* algebra to Banach algebras , هفتمین سمينار آناليز تابعی و كاربردهاي آن