Toeplitz Algebras of Correspondences and Endomorphisms of Sums of Type I Factors

Philip M. Gipson

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arXiv · 1711.04835

Toeplitz Algebras of Correspondences and Endomorphisms of Sums of Type I Factors

Philip M. Gipson

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Abstract

It is a well-known fact that endomorphisms of $B(H)$ are intimately connected with families of mutually orthogonal isometries, i.e. with representations of the so-called Toeplitz $C^*$-algebras. In this paper we consider a natural generalization of this connection between the representation theory of certain $C^*$-algebras associated to graphs and endomorphisms of certain von Neumann subalgebras of $B(H)$. Our primary results give criteria by which it may be determined if two representations give rise to equal or conjugate endomorphisms.

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Philip M. Gipson. 2017-11-13. Toeplitz Algebras of Correspondences and Endomorphisms of Sums of Type I Factors. https://arxiv.org/abs/1711.04835

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