{"paper":{"title":"Second quantization and the L^p-spectrum of nonsymmetric Ornstein-Uhlenbeck operators","license":"","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Jan van Neerven","submitted_at":"2005-09-26T11:25:29Z","abstract_excerpt":"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 $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0509057","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}