B*‐algebra representations in a quaternionic Hilbert module

1983 ◽  
Vol 24 (12) ◽  
pp. 2780-2782 ◽  
Author(s):  
A. Soffer ◽  
L. P. Horwitz
Keyword(s):  
Hilbert Module

A Hilbert Module Approach to the Haagerup Property

2012 ◽  
Vol 73 (3) ◽  
pp. 431-454 ◽  
Author(s):  
Zhe Dong ◽  
Zhong-Jin Ruan
Keyword(s):  
Hilbert Module ◽  
Haagerup Property

scholarly journals A SIMPLE PROOF OF THE FUNDAMENTAL THEOREM ABOUT ARVESON SYSTEMS

2006 ◽  
Vol 09 (02) ◽  
pp. 305-314 ◽  
Author(s):  
MICHAEL SKEIDE
Keyword(s):  
Hilbert Space ◽  
Simple Proof ◽  
Fundamental Theorem ◽  
Hilbert Module ◽  
Bounded Operators ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Product Systems ◽  
Dimensional Hilbert Space ◽  
The One

With every E0-semigroup (acting on the algebra of of bounded operators on a separable infinite-dimensional Hilbert space) there is an associated Arveson system. One of the most important results about Arveson systems is that every Arveson system is the one associated with an E0-semigroup. In these notes we give a new proof of this result that is considerably simpler than the existing ones and allows for a generalization to product systems of Hilbert module (to be published elsewhere).

scholarly journals RELATIVE TORSION

2001 ◽  
Vol 03 (01) ◽  
pp. 15-85 ◽  
Author(s):  
DAN BURGHELEA ◽  
LEONID FRIEDLANDER ◽  
THOMAS KAPPELER
Keyword(s):  
Fundamental Group ◽  
Finite Type ◽  
Von Neumann Algebra ◽  
Hilbert Module ◽  
Von Neumann ◽  
Geometric Invariants ◽  
Finite Dimensional ◽  
Finite Von Neumann Algebra ◽  
Special Cases ◽  
Relative Torsion

This paper achieves, among other things, the following: • It frees the main result of [9] from the hypothesis of determinant class and extends this result from unitary to arbitrary representations. • It extends (and at the same times provides a new proof of) the main result of Bismut and Zhang [3] from finite dimensional representations of Γ to representations on an [Formula: see text]-Hilbert module of finite type ([Formula: see text] a finite von Neumann algebra). The result of [3] corresponds to [Formula: see text]. • It provides interesting real valued functions on the space of representations of the fundamental group Γ of a closed manifold M. These functions might be a useful source of topological and geometric invariants of M. These objectives are achieved with the help of the relative torsion ℛ, first introduced by Carey, Mathai and Mishchenko [12] in special cases. The main result of this paper calculates explicitly this relative torsion (cf. Theorem 1.1).

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