کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4591798 | 1335054 | 2009 | 24 صفحه PDF | دانلود رایگان |
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.
Journal: Journal of Functional Analysis - Volume 256, Issue 6, 15 March 2009, Pages 1669-1692