TY  - GEN
T1  - Samuel multiplicity and Fredholm theory
A1  - Eschmeier,Jörg
Y1  - 2012/03/09
N2  - 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.
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2012/4639
ER  -