Invertibility in Fréchet algebras (Q818553)

The main result of the paper states a characterization of the joint left spectrum over a Banach space \(X\) for tensor products of unital Fréchet algebras \({\mathcal A,B}\). Among other applications, the results are used to generalize Allan's theorem on invertibility of holomorphic functions with values in a Banach algebra to the case of infinite-dimensional domains and to an infinite number of functions.