Journal of Operator Theory

Volume 44, Issue 1, Summer 2000 pp. 113-138.

Endomorphisms of

$\cal B \cal H$ , extensions of pure states, and a class of representations of

${\cal O}_n$

Authors: Neal J. Fowler (1), and Marcelo Laca (2)
Author institution: (1) Department of Mathematics, University of Newcastle, Callaghan, NSW 2308, Australia
(2) Department of Mathematics, University of Newcastle, Callaghan, NSW 2308, Australia

Summary: We construct the pure states of

${\cal O}_n$ that extend a given pure state of the fixed point algebra

${\cal F}_n$ of the gauge action, and we show that the gauge group acts transitively on these extensions. We apply this to construct and classify the ergodic endomorphisms of

${\cal B}({\cal H})$ whose tail algebra has a minimal projection. We discuss examples arising from product states of

${\cal F}_n$ and from the trace on the Choi subalgebra of

${\cal O}_n$ .

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