Certain dense subalgebras of continuous vector-valued operator algebras

Mathematical Analysis and its Contemporary Applications

دوره 2، شماره 1، تیر 2020، صفحه 28-34   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/maca.2020.679855

نویسنده

Abbasali Shokri^*

Department of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran.

چکیده

Let X be a compact metric space with at least two elements, B be a unital commutative Banach algebra over the scalar field F=R or C, and α in R with 0<α≤1. Suppose that C(X,B) be the continuous, A(X,B) be the analytic, and Lip_α(X,B) be the α-Lipschitz B-valued operator algebras on X. In this paper, we prove that the algebras Lip _α(X,B) and A(X,B) are dense in C(X,B) under sup-norm. Also, we study the relationship between elements of the algebras Lip _α(X,B) and A(X,B).

کلیدواژه‌ها

Dense؛ Banach algebra؛ Lipschitz algebra؛ Vector-valued operator