A Dixmier type averaging property of automorphisms on a C∗-Algebra

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A Dixmier type averaging property of automorphisms on a C∗-Algebra. / Rørdam, Mikael.

I: International Journal of Mathematics, Bind 34, Nr. 4, 2350017, 2023.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Rørdam, M 2023, 'A Dixmier type averaging property of automorphisms on a C∗-Algebra', International Journal of Mathematics, bind 34, nr. 4, 2350017. https://doi.org/10.1142/S0129167X23500179

APA

Rørdam, M. (2023). A Dixmier type averaging property of automorphisms on a C∗-Algebra. International Journal of Mathematics, 34(4), [2350017]. https://doi.org/10.1142/S0129167X23500179

Vancouver

Rørdam M. A Dixmier type averaging property of automorphisms on a C∗-Algebra. International Journal of Mathematics. 2023;34(4). 2350017. https://doi.org/10.1142/S0129167X23500179

Author

Rørdam, Mikael. / A Dixmier type averaging property of automorphisms on a C∗-Algebra. I: International Journal of Mathematics. 2023 ; Bind 34, Nr. 4.

Bibtex

@article{6261d1c1a25d4a358bd40d25f53b148d,
title = "A Dixmier type averaging property of automorphisms on a C∗-Algebra",
abstract = "In this study of the relative Dixmier property for inclusions of von Neumann algebras and of C?-Algebras, Popa considered a certain property of automorphisms on C?-Algebras, that we here call the strong averaging property. In this paper, we characterize when an automorphism on a C?-Algebra has the strong averaging property. In particular, automorphisms on commutative C?-Algebras possess this property precisely when they are free. An automorphism on a unital separable simple C?-Algebra with at least one tracial state has the strong averaging property precisely when its extension to the finite part of the bi-dual of the C?-Algebra is properly outer, and in the simple, non-Tracial case the strong averaging property is equivalent to being outer. To illustrate the usefulness of the strong averaging property we give three examples where we can provide simpler proofs of existing results on crossed product C?-Algebras, and we are also able to extend these results in different directions. ",
keywords = "Automorphisms on C-Algebras, inclusions of C-Algebras, the Dixmier property",
author = "Mikael R{\o}rdam",
note = "Publisher Copyright: {\textcopyright} 2023 World Scientific Publishing Company.",
year = "2023",
doi = "10.1142/S0129167X23500179",
language = "English",
volume = "34",
journal = "International Journal of Mathematics",
issn = "0129-167X",
publisher = "World Scientific Publishing Co. Pte. Ltd.",
number = "4",

}

RIS

TY - JOUR

T1 - A Dixmier type averaging property of automorphisms on a C∗-Algebra

AU - Rørdam, Mikael

N1 - Publisher Copyright: © 2023 World Scientific Publishing Company.

PY - 2023

Y1 - 2023

N2 - In this study of the relative Dixmier property for inclusions of von Neumann algebras and of C?-Algebras, Popa considered a certain property of automorphisms on C?-Algebras, that we here call the strong averaging property. In this paper, we characterize when an automorphism on a C?-Algebra has the strong averaging property. In particular, automorphisms on commutative C?-Algebras possess this property precisely when they are free. An automorphism on a unital separable simple C?-Algebra with at least one tracial state has the strong averaging property precisely when its extension to the finite part of the bi-dual of the C?-Algebra is properly outer, and in the simple, non-Tracial case the strong averaging property is equivalent to being outer. To illustrate the usefulness of the strong averaging property we give three examples where we can provide simpler proofs of existing results on crossed product C?-Algebras, and we are also able to extend these results in different directions.

AB - In this study of the relative Dixmier property for inclusions of von Neumann algebras and of C?-Algebras, Popa considered a certain property of automorphisms on C?-Algebras, that we here call the strong averaging property. In this paper, we characterize when an automorphism on a C?-Algebra has the strong averaging property. In particular, automorphisms on commutative C?-Algebras possess this property precisely when they are free. An automorphism on a unital separable simple C?-Algebra with at least one tracial state has the strong averaging property precisely when its extension to the finite part of the bi-dual of the C?-Algebra is properly outer, and in the simple, non-Tracial case the strong averaging property is equivalent to being outer. To illustrate the usefulness of the strong averaging property we give three examples where we can provide simpler proofs of existing results on crossed product C?-Algebras, and we are also able to extend these results in different directions.

KW - Automorphisms on C-Algebras

KW - inclusions of C-Algebras

KW - the Dixmier property

UR - http://www.scopus.com/inward/record.url?scp=85150688538&partnerID=8YFLogxK

U2 - 10.1142/S0129167X23500179

DO - 10.1142/S0129167X23500179

M3 - Journal article

AN - SCOPUS:85150688538

VL - 34

JO - International Journal of Mathematics

JF - International Journal of Mathematics

SN - 0129-167X

IS - 4

M1 - 2350017

ER -

ID: 359610489