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Abstract

Let $A$ be a commutative Banach algebra and let ${\mit\Sigma} _{A}$ be its structure space$.$ The norm spectrum $\sigma ( f) $ of the functional $f\in A^{\ast }$ is defined by $ \sigma ( f) =\overline{\{ f\cdot a:a\in A\} }\cap {\mit\Sigma} _{A},$ where $f\cdot a$ is the functional on $A$ defined by $ \langle f\cdot a,b\rangle =\langle f,ab\rangle $, $b\in A.$ We investigate basic properties of the norm spectrum in certain classes of commutative Banach algebras and present some applications.