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

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Resumé

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.
OriginalsprogEngelsk
TidsskriftJournal of Functional Analysis
Vol/bind272
Udgave nummer2
Sider (fra-til)759-775
ISSN0022-1236
DOI
StatusUdgivet - 2017

Fingeraftryk

Cuntz Algebra
Commutant
Endomorphisms
Subalgebra

Citer dette

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title = "On endomorphisms of the Cuntz algebra which preserve the canonical UHF-subalgebra, II",
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",
author = "Tomohiro Hayashi and Hong, {Jeong Hee} and Wojciech Szymanski",
year = "2017",
doi = "10.1016/j.jfa.2016.07.004",
language = "English",
volume = "272",
pages = "759--775",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Heinemann",
number = "2",

}

On endomorphisms of the Cuntz algebra which preserve the canonical UHF-subalgebra, II. / Hayashi, Tomohiro; Hong, Jeong Hee; Szymanski, Wojciech.

I: Journal of Functional Analysis, Bind 272, Nr. 2, 2017, s. 759-775.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

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

Y1 - 2017

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

U2 - 10.1016/j.jfa.2016.07.004

DO - 10.1016/j.jfa.2016.07.004

M3 - Journal article

VL - 272

SP - 759

EP - 775

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 2

ER -