An additive formula for Samuel multiplicities on Hilbert spaces of analytic functions |
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Authors: | Guozheng Cheng Xiang Fang |
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Affiliation: | a School of Mathematics, Wenzhou University, Wenzhou, Zhejiang, 325035, China b Department of Mathematics, Kansas State University, Manhattan, KS 6650, United States |
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Abstract: | We establish a short exact sequence to relate the germ model of invariant subspaces of a Hilbert space of vector-valued analytic functions and the sheaf model of the corresponding coinvariant subspaces. As a consequence we obtain an additive formula for Samuel multiplicities. As an application, we give a different proof for a formula relating the fibre dimension and the Samuel multiplicity which is first proved in Fang (2005) [11]. The feature of the new proof is that the analytic arguments in Fang (2005) [11] are now subsumed by algebraic machinery. |
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Keywords: | Samuel multiplicity Fibre dimension Sheaf model Germ model |
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