Endomorphisms of B(H)

1994/08/29 by Bratteli, Ola, Jorgensen, Palle, Price, Geoff
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.funct-an/9408001

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 nⁱnfinity. 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.

Related

• Endomorphisms of B(H), extensions of pure states, and a class of representations of O_n
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• Classification of sectors of the Cuntz algebras by graph invariants
• Automorphisms of the Cuntz algebras
• On Invariant MASAs for Endomorphisms of the Cuntz Algebras