Co-actions, Isometries and isomorphism classes of Hilbert modules
Operator Algebras
2023-06-28 v1
Abstract
We show that a A-linear map of Hilbert A-modules is induced by a unitary Hilbert module operator if and only if it extends to an ordinary unitary on appropriately defined enveloping Hilbert spaces. Applications to the theory of multiplicative unitaries compute the equivalence classes of Hilbert modules over a class of C*- algebraic quantum groups. We thus develop a theory that for example could be used to show non-existence of certain co-actions. In particular, we show that the Cuntz semigroup functor takes a co-action to a multiplicative action.
Keywords
Cite
@article{arxiv.2306.15158,
title = {Co-actions, Isometries and isomorphism classes of Hilbert modules},
author = {Dan Z. Kucerovsky},
journal= {arXiv preprint arXiv:2306.15158},
year = {2023}
}