Journal of Operator Theory

Volume 60, Issue 2, Fall 2008 pp. 399-414.

Samuel multiplicity for several commuting operators

Authors: Joerg Eschmeier
Author institution: Department of Mathematics, Saarland University, 66041 Saarbruecken, Postfach 15 11 50, Germany

Summary: In this paper we show that the Samuel multiplicity of a lower semi-Fredholm tuple $T \in L(X)^n$ of commuting bounded operators on a complex Banach space $X$ coincides with the generic dimension of the last cohomology groups $H^n(z-T,X)$ of its Koszul complex near $z = 0.$ As applications we show that the algebraic and analytic Samuel multiplicities of $T$ coincide and that the Samuel multiplicity is additive for closed invariant subspaces of the symmetric Fock space.

Keywords: Fredholm tuples, Samuel multiplicity, Koszul complex.

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