Unitary invariants for Hilbert modules of finite rank
ثبت نشده
چکیده
We associate a sheaf model to a class of Hilbert modules satisfying a natural finiteness condition. It is obtained as the dual to a linear system of Hermitian vector spaces (in the sense of Grothendieck). A refined notion of curvature is derived from this construction leading to a new unitary invariant for the Hilbert module. A division problem with bounds, originating in Douady’s privilege, is related to this framework. A series of concrete computations illustrate the abstract concepts of the paper.
منابع مشابه
Multi-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules
In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective ...
متن کاملHilbert modules and modules over finite von Neumann algebras and applications to L2-invariants
Throughout this paper A is a finite von Neumann algebra and tr :A −→ C is a finite normal faithful trace. Recall that a von Neumann algebra is finite if and only if it possesses such a trace. Let l2(A) be the Hilbert space completion of A which is viewed as a pre-Hilbert space by the inner product 〈a, b〉 = tr(ab∗). A finitely generated Hilbert A-module V is a Hilbert space V together with a lef...
متن کاملm at h . FA ] 1 2 O ct 2 00 6 EQUIVALENCE OF QUOTIENT HILBERT MODULES – II RONALD
For any open, connected and bounded set Ω ⊆ C m , let A be a natural function algebra consisting of functions holomorphic on Ω. Let M be a Hilbert module over the algebra A and M0 ⊆ M be the submodule of functions vanishing to order k on a hypersurface Z ⊆ Ω. Recently the authors have obtained an explicit complete set of unitary invariants for the quotient module Q = M ⊖ M0 in the case of k = 2...
متن کاملDilations for $C^ast$-dynamical systems with abelian groups on Hilbert $C^ast$-modules
In this paper we investigate the dilations of completely positive definite representations of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules. We show that if ((mathcal{A}, G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group, then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}, G,alpha)) on a Hilbert ...
متن کاملEquivalence of quotient Hilbert modules
Let M be a Hilbert module of holomorphic functions over a natural function algebra A (Ω), where Ω ⊆Cm is a bounded domain. Let M0 ⊆M be the submodule of functions vanishing to order k on a hypersurface Z ⊆ Ω. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient modules Q = M ⊖M0. The invariants are given explicitly in the particula...
متن کامل