Equivalence of quotient Hilbert modules

2003/10/17 by Ronald G. Douglas, Gadadhar Misra
Mathematics · #math.FA #math.OA

paper · pdf

published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 3, August 2003, pp. 281-291 · 11 pages

arxiv created 2003/10/17 · arxiv updated 2009/12/01

Abstract

Let \clM be a Hilbert module of holomorphic functions over a natural function algebra A(Ω), where Ω⊆ \bbC^m is a bounded domain. Let \clM₀⊆ \clM be the submodule of functions vanishing to order k on a hypersurface \clZ ⊆ Ω. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient modules \clQ=\clM \ominus \clM₀. The invariants are given explicitly in the particular case of k = 2.

Related

• Equivalence of quotient Hilbert modules -- II
• On unitary invariants of quotient Hilbert modules along smooth complex analytic sets
• Unitary invariants for Hilbert modules of finite rank
• Quotients of Standard Hilbert Modules
• Quasi-free resolutions of Hilbert modules