On Equivalence for Representations of Toeplitz Algebras

Abstract

Two new notions of equivalence for representations of a Toeplitz algebra ${\mathcal{E}}_n$, $n<\infty$, on a common Hilbert space are defined. Our main results apply to $C^{\ast }$-dynamics and the conjugacy of certain $\ast$-endomorphisms. One particular case of the relations is shown to coincide with the multiplicity of a representation. Previously known results due to Laca and Enomoto-Watatani are recovered as special cases.

arXiv comment13 pages. Minor revisions