The norm spectrum in certain classes of commutative Banach algebras

H. S. Mustafayev¹

¹ Department of Mathematics Faculty of Sciences Yuzuncu Yil University 65080, Van, Turkey

Colloquium Mathematicum, Tome 123 (2011) no. 1, pp. 95-114

Résumé

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.

Détail

DOI : 10.4064/cm123-1-7

Keywords: commutative banach algebra mit sigma its structure space norm spectrum sigma functional ast defined sigma overline cdot cap mit sigma where cdot functional defined langle cdot rangle langle rangle investigate basic properties norm spectrum certain classes commutative banach algebras present applications