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- W2094380234 abstract "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." @default.
- W2094380234 created "2016-06-24" @default.
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- W2094380234 date "2009-03-01" @default.
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- W2094380234 title "The Fredholm index of a pair of commuting operators, II" @default.
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- W2094380234 doi "https://doi.org/10.1016/j.jfa.2009.01.024" @default.
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