On endomorphisms of the Cuntz algebra which preserve the canonical UHF-subalgebra, II

Tomohiro Hayashi; Jeong Hee Hong; Wojciech Szymanski

doi:10.1016/j.jfa.2016.07.004

On endomorphisms of the Cuntz algebra which preserve the canonical UHF-subalgebra, II

Tomohiro Hayashi, Jeong Hee Hong, Wojciech Szymanski

Institut for Matematik og Datalogi

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

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Abstract

It was shown recently by Conti, Rørdam and Szymanskithat there exist exndomorphisms λ_uof the Cuntz algebra O_n such that λ_u(F_n) is contained in F_n but u does not belong to F_n, and a question was raised if for such a u there must always exist a unitary v in F_n with λ_u|_F_n = λ_v|_F_n. In the present paper, we answer this question to the negative. To this end, we analyze the structure of such endomorphisms λ_u for which the relative commutant of λ_u(F_n) in F_n is finite dimensional.

Originalsprog	Engelsk
Tidsskrift	Journal of Functional Analysis
Vol/bind	272
Udgave nummer	2
Sider (fra-til)	759-775
ISSN	0022-1236
DOI	https://doi.org/10.1016/j.jfa.2016.07.004
Status	Udgivet - 15. jan. 2017

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10.1016/j.jfa.2016.07.004

On endomorphisms of the Cuntz algebra which preserve the canonical UHF-subalgebra, IIIndsendt manuskript, 221 KB

https://arxiv.org/pdf/1603.09044.pdf

Citationsformater

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abstract = "It was shown recently by Conti, R{\o}rdam and Szymanskithat there exist exndomorphisms λ_uof the Cuntz algebra O_n such that λ_u(F_n) is contained in F_n but u does not belong to F_n, and a question was raised if for such a u there must always exist a unitary v in F_n with λ_u|_F_n = λ_v|_F_n. In the present paper, we answer this question to the negative. To this end, we analyze the structure of such endomorphisms λ_u for which the relative commutant of λ_u(F_n) in F_n is finite dimensional. ",

keywords = "Cuntz algebra, endomorphism, UHF-subalgebra, Endomorphism",

author = "Tomohiro Hayashi and Hong, {Jeong Hee} and Wojciech Szymanski",

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T1 - On endomorphisms of the Cuntz algebra which preserve the canonical UHF-subalgebra, II

AU - Hayashi, Tomohiro

AU - Hong, Jeong Hee

AU - Szymanski, Wojciech

PY - 2017/1/15

Y1 - 2017/1/15

N2 - It was shown recently by Conti, Rørdam and Szymanskithat there exist exndomorphisms λ_uof the Cuntz algebra O_n such that λ_u(F_n) is contained in F_n but u does not belong to F_n, and a question was raised if for such a u there must always exist a unitary v in F_n with λ_u|_F_n = λ_v|_F_n. In the present paper, we answer this question to the negative. To this end, we analyze the structure of such endomorphisms λ_u for which the relative commutant of λ_u(F_n) in F_n is finite dimensional.

AB - It was shown recently by Conti, Rørdam and Szymanskithat there exist exndomorphisms λ_uof the Cuntz algebra O_n such that λ_u(F_n) is contained in F_n but u does not belong to F_n, and a question was raised if for such a u there must always exist a unitary v in F_n with λ_u|_F_n = λ_v|_F_n. In the present paper, we answer this question to the negative. To this end, we analyze the structure of such endomorphisms λ_u for which the relative commutant of λ_u(F_n) in F_n is finite dimensional.

KW - Cuntz algebra

KW - endomorphism

KW - UHF-subalgebra

KW - Endomorphism

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DO - 10.1016/j.jfa.2016.07.004

M3 - Journal article

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VL - 272

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JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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ER -

On endomorphisms of the Cuntz algebra which preserve the canonical UHF-subalgebra, II

Abstract

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