Operator *-correspondences in analysis and geometry
Abstract
An operator *-algebra is a non-selfadjoint operator algebra with completely isometric involution. We show that any operator *-algebra admits a faithful representation on a Hilbert space in such a way that the involution coincides with the operator adjoint up to conjugation by a symmetry. We introduce operator *-correspondences as a general class of inner product modules over operator *-algebras and prove a similar representation theorem for them. From this we derive the existence of linking operator *-algebras for operator *-correspondences. We illustrate the relevance of this class of inner product modules by providing numerous examples arising from noncommutative geometry.
Cite
@article{arxiv.1703.10063,
title = {Operator *-correspondences in analysis and geometry},
author = {David Blecher and Jens Kaad and Bram Mesland},
journal= {arXiv preprint arXiv:1703.10063},
year = {2019}
}
Comments
31 pages. This work originated from the MFO workshop "Operator spaces and noncommutative geometry in interaction"