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Endomorphisms of B(H)

Ola Bratteli·Palle Jorgensen·Geoff Price
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Abstract

The unital endomorphisms of B(H) of (Powers) index n are classified by certain U(n)-orbits in the set of non-degenerate representations of the Cuntz algebra O_n on H. Using this, the corre- sponding conjugacy classes are identified, and a set of labels is given. This set is given as P modulo a certain non-smooth equivalence, where P is a set of pure state on the UHF algebra of Glimm type n^infinity. Several subsets of P, giving concrete examples of non- conjugate shifts, are worked out in detail, including sets of product states, and a set of nearest neighbor states.

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Ola Bratteli, Palle Jorgensen, Geoff Price. 1994-08-30. Endomorphisms of B(H). https://arxiv.org/abs/funct-an/9408001

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