Some Absolutely Continuous Representations of Function Algebras

Abstract

In this paper we study some absolutely continuous representations of function algebras, which are weak ρ-spectral in the sense of [5] and [6], for a scalar ρ > 0. Precisely we investigate certain conditions for the existence of a spectral ρ-dilation of such representation. Among others we obtain different results which generalize the corresponding theorems of D. Gaspar

Keywords

• Uniform algebra
• Representation
• Spectral dilation