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

Jan van Neerven
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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 $L$.

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Jan van Neerven. 2005-09-26. Second quantization and the L^p-spectrum of nonsymmetric Ornstein-Uhlenbeck operators. https://arxiv.org/abs/math-ph/0509057

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