Please use this identifier to cite or link to this item: doi:10.22028/D291-26335
Title: Samuel multiplicity and Fredholm theory
Author(s): Eschmeier, Jörg
Language: English
Year of Publication: 2006
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: In this note we prove that, for a given Fredholm tuple T=(T_{1},...,T_{n}) of commuting bounded operators on a complex Banach space X, the limits c_{p}(T)=\lim_{k\rightarrow\infty}\dim H^{p}(T^{k},X)/k^{n} exist and calculate the generic dimension of the cohomology groups H^{p}(z-T,X) of the Koszul complex of T near z = 0. To deduce this result we show that the above limits coincide with the Samuel multiplicities of the stalks of the cohomology sheaves H^{p}(z-T,\mathcal{O}_{\mathbb{C}^{n}}^{X}) of the associated complex of analytic sheaves at z = 0.
Link to this record: urn:nbn:de:bsz:291-scidok-46392
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 173
Date of registration: 9-Mar-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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