Spectrum of operators in ideal spaces

Abstract

One considers “weighted translation” operators in ideal Banach spaces. It is proved that if the translation is aperiodic (the set of periodic points has measure zero), then the spectrum of such an operator is rotationinvariant. This result can be extended (under certain additional restrictions) to “weighted translation” operators acting in regular subspaces of ideal spaces, in particular, to operators in Hardy spaces.

In this note we prove the rotation-invariance of the spectrum of aperiodic operators of “weighted translation” in ideal spaces and uniform B-algebras.