On localized automorphisms of the Cuntz algebras which preserve the diagonal subalgebra

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Abstract

In 1978, Cuntz raised the problem of classifying automorphisms of On which leave both the diagonal and the core UHF-subalgebra invariant. In this note, we start developing a machinery that might be useful towards this goal. In particular, we give a practical criterion of invertibility of endomorphisms of On corresponding to unitaries in the normalizer of the diagonal inside the UHF-subalgebra. We also analyze the action of such localized automorphisms on the spectrum of the diagonal thus obtaining criteria of outerness.
Original languageEnglish
Title of host publicationNew development of Operator Algebras
EditorsKengo Matsumoto
Number of pages7
Volume1587
Publication date2008
Pages109-115
Publication statusPublished - 2008
Externally publishedYes
EventNew development of Operator Algebras - Kyoto, Japan
Duration: 10. Sept 200712. Sept 2007

Conference

ConferenceNew development of Operator Algebras
Country/TerritoryJapan
CityKyoto
Period10/09/200712/09/2007
SeriesR.I.M.S. Kokyuroku
Number1587
ISSN1880-2818

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