Endomorphisms of O_n which preserve the canonical UHF-subalgebra

Details Endomorphisms of O_n which preserve the canonical UHF-subalgebra Endomorphisms of O_n which preserve the canonical UHF-subalgebra

2009-10-07

arxiv.org/abs/0910.1304v1

J. Funct. Anal. 259, 602-617 (2010)

Mathematics

Operator Algebras

1 figure, requires prepictex.tex, pictex.tex, postpictex.tex

Scientific paper

Unital endomorphisms of the Cuntz algebra O_n which preserve the canonical UHF-subalgebra F_n of O_n are investigated. We give examples of such endomorphisms for which the associated unitary element in O_n does not belong to F_n. One such example, in the case where n=2, arises from a construction of a unital endomorphism on O_2 which preserves the canonical UHF-subalgebra and where the relative commutant of the image in O_2 contains a copy of O_2.

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