Path-connected Closures of Unitary Orbits
Operator Algebras
2020-08-11 v1
Abstract
Suppose A and B are unital C*-algebras and A is separable. Let Rep(A,B) denote the set of all unital *-homomorphisms from A to B with the topology of pointwise convergence. We consider the problem of when the closure of the unitary orbit of a single representation in Rep(A,B) is path-connected. An affirmative answer was given by the first author when A is singly generated and B is the algebra of all operators on a separable Hilbert space. We extend this result for all separable A. We also give an affirmative answer when A is AF or homogeneous and B is a von Neumann algebra or when A is ASH and B is a finite von Neumann algebra.
Cite
@article{arxiv.2008.03583,
title = {Path-connected Closures of Unitary Orbits},
author = {Don Hadwin and Wenjing Liu},
journal= {arXiv preprint arXiv:2008.03583},
year = {2020}
}