Endomorphisms of O_n which preserve the canonical UHF-subalgebra

Mikael Rørdam; Wojciech Szymanski; Roberto Conti

Endomorphisms of O_n which preserve the canonical UHF-subalgebra

Mikael Rørdam, Wojciech Szymanski, Roberto Conti

Department of Mathematical Sciences

17 Citations (Scopus)

Abstract

Unital endomorphisms of the Cuntz algebra O_n which preserve the canonical UHF-subalgebra F_n⊆O_n are investigated. We give examples of such endomorphisms λ=λ_u for which the associated unitary element u in On (which satisfies λ(S_j)=uS_j for all j) does not belong to F_n. One such example, in the case where n=2, arises from a construction of a unital endomorphism on O₂ which preserves the canonical UHF-subalgebra and where the relative commutant of its image in O₂ contains a copy of O₂.

Original language	English
Journal	Journal of Functional Analysis
Volume	259
Pages (from-to)	602-617
Number of pages	16
ISSN	0022-1236
Publication status	Published - Aug 2010

Cite this

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title = "Endomorphisms of O_n which preserve the canonical UHF-subalgebra",

abstract = "Unital endomorphisms of the Cuntz algebra On which preserve the canonical UHF-subalgebra Fn⊆On are investigated. We give examples of such endomorphisms λ=λu for which the associated unitary element u in On (which satisfies λ(Sj)=uSj for all j) does not belong to Fn. One such example, in the case where n=2, arises from a construction of a unital endomorphism on O2 which preserves the canonical UHF-subalgebra and where the relative commutant of its image in O2 contains a copy of O2.",

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T1 - Endomorphisms of O_n which preserve the canonical UHF-subalgebra

AU - Rørdam, Mikael

AU - Szymanski, Wojciech

AU - Conti, Roberto

PY - 2010/8

Y1 - 2010/8

N2 - Unital endomorphisms of the Cuntz algebra On which preserve the canonical UHF-subalgebra Fn⊆On are investigated. We give examples of such endomorphisms λ=λu for which the associated unitary element u in On (which satisfies λ(Sj)=uSj for all j) does not belong to Fn. One such example, in the case where n=2, arises from a construction of a unital endomorphism on O2 which preserves the canonical UHF-subalgebra and where the relative commutant of its image in O2 contains a copy of O2.

AB - Unital endomorphisms of the Cuntz algebra On which preserve the canonical UHF-subalgebra Fn⊆On are investigated. We give examples of such endomorphisms λ=λu for which the associated unitary element u in On (which satisfies λ(Sj)=uSj for all j) does not belong to Fn. One such example, in the case where n=2, arises from a construction of a unital endomorphism on O2 which preserves the canonical UHF-subalgebra and where the relative commutant of its image in O2 contains a copy of O2.

M3 - Journal article

SN - 0022-1236

VL - 259

SP - 602

EP - 617

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

ER -

Endomorphisms of O_n which preserve the canonical UHF-subalgebra

Abstract

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