Closed operator functional calculus in Banach modules and applications

Abstract

We describe a closed operator functional calculus in Banach modules over the group algebra $L^1(\mathbb{R})$ and illustrate its usefulness with a few applications. In particular, we deduce a spectral mapping theorem for operators in the functional calculus, which generalizes some of the known results. We also obtain an estimate for the spectrum of a perturbed differential operator in a certain class.

References in corpus (2)

• Memory Estimation of Inverse Operators
• Similarity Techniques in the Spectral Analysis of Perturbed Operator Matrices

Cited by in corpus (1)

• Kadec-type theorems for sampled group orbits