Second quantization and the L^p-spectrum of nonsymmetric Ornstein-Uhlenbeck operators

Abstract

The spectra of the second quantization and the symmetric second quantization of a strict Hilbert space contraction are computed explicitly and shown to coincide. As an application, we compute the spectrum of the nonsymmetric Ornstein-Uhlenbeck operator $L$ associated with the infinite-dimensional Langevin equation $$dU(t)=AU(t)dt+dW(t),$$ where $A$ is the generator of a strongly continuous semigroup on a Banach space $E$ and $W$ is a cylindrical Wiener process in $E$. In the case of a finite-dimensional space $E$ we recover the recent Metafune-Pallara-Priola formula for the spectrum of $L$.

arXiv comment20 pages

Cited by in corpus (1)

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