The Fredholm index of a pair of commuting operators. II
The author continues to study a method to calculate the Fredholm index of a pair of commuting operators [for Part~I, see Geom.\ Funct.\ Anal.\ 16, No.\,2, 367--402 (2006; Zbl 1105.47008)]. He shows first that an inequality obtained by \textit{R.\,G.\thinspace Douglas} and \textit{K.--R.\thinspace Yan} [Indiana Univ.\ Math.\ J.\ 42, No.\,3, 811--820 (1993; Zbl 0808.46068)] on Hilbert modules is actually equality. This result leads to a proof of the semi-continuity of the generalized Samuel multiplicities for a pair of commuting operators. As an application, it is shown that the Samuel additivity formula on Hilbert spaces of holomorphic functions is equivalent to a generalized Gleason problem, leading in turn to the additivity of Samuel multiplicity on the symmetric Fock space.
scientific article; zbMATH DE number 5541656
scientific article