Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591798 | Journal of Functional Analysis | 2009 | 24 Pages |
We first show that an inequality on Hilbert modules, obtained by Douglas and Yan in 1993, is always an equality. This allows us to establish the semi-continuity of the generalized Samuel multiplicities for a pair of commuting operators. Then we discuss the general structure of a Fredholm pair, aiming at developing a model theory. For application we prove that the Samuel additivity formula on Hilbert spaces of holomorphic functions is equivalent to a generalized Gleason problem. As a consequence it follows the additivity of Samuel multiplicity, in its full generality, on the symmetric Fock space. During the course we discover that a variant e′(⋅) of the classic algebraic Samuel multiplicity might be more suitable for Hilbert modules and can lead to better results.