Spectral Properties and Stability in Vector-Valued Lipschitz Algebras

Let  A be a commutative Banach algebra and (K,d) be a compact metric space. In this paper, we examine various spectral properties, including the unique uniform norm property, weak regularity, Ditkin's condition and local operators, within the context of vector-valued Lipschitz algebras denoted as \mathrm{Lip}(K,A).  We demonstrate that the aforementioned concepts exhibit stability between A and \mathrm{Lip}(K,A). Furthermore, we establish that a commutative Banach algebra A is classified as a Tauberian algebra if and only if \mathrm{Lip}(K,A) is also a Tauberian algebra.

کلیدواژه ها:

character ، Commutative Banach algebra ، Ditkin's condition ، Lipschitz algebra ، Local operator ، Spectral property ، Tauberian algebra ، Unique uniform norm property ، vector-valued Lipcshitz algebra ، weak regularity