Lipschitzness of *-homomorphisms between C*-metric algebras

Wei Wu

Lipschitzness of -homomorphisms between C-metric algebras

Operator Algebras 2009-01-23 v2

Authors: Wei Wu

Abstract

A C*-metric algebra consists of a unital C*-algebra and a Leibniz Lip-norm on the C*-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital *-homomorphism from a C*-metric algebra to another one is necessarily Lipschitz. It results that the free product of two Lipschitz unital *-homomorphisms between C*-metric algebras coming from *-filtrations is still a Lipschitz unital *-homomorphism.

Keywords

c*-algebras hilbert modules graph algebras

Cite

@article{arxiv.0901.2695,
  title  = {Lipschitzness of *-homomorphisms between C*-metric algebras},
  author = {Wei Wu},
  journal= {arXiv preprint arXiv:0901.2695},
  year   = {2009}
}

Comments

10 pages. *-homomorphism between C*-metric algebras added to Definition 2.5. An error in Proposition 3.2 is corrected. A few minor improvements elsewhere