L1-spectrum of Banach space valued Ornstein-Uhlenbeck operators

TL;DR

This paper characterizes the L^1-spectrum of Ornstein-Uhlenbeck operators in infinite-dimensional Banach spaces, extending recent results by analyzing the spectrum with a nonempty point spectrum of the drift operator.

Contribution

It provides a comprehensive spectral characterization of Ornstein-Uhlenbeck operators in Banach spaces with nonempty point spectrum, generalizing previous findings.

Findings

Spectrum characterized for infinite-dimensional Banach spaces

Extension of recent spectral results

Applicable when the drift operator has nonempty point spectrum

Abstract

We characterize the $L^1(E;\mu_\infty)$-spectrum of the Ornstein-Uhlenbeck operator, where $\mu_\infty$ is the invariant measure for the Ornstein-Uhlenbeck semigroup. The main result covers the general case of an infinite-dimensional Banach space E under the assumption that the point spectrum of drift operator $A^*$ is nonempty. This extends several recent related results.