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 hdl:20.500.11880/26391 http://dx.doi.org/10.22028/D291-26335 |
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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preprint_173_06.pdf | 158,77 kB | Adobe PDF | View/Open |
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