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Singly generated operator algebras satisfying weakened versions of amenability

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter

Published

Standard

Singly generated operator algebras satisfying weakened versions of amenability. / Choi, Yemon.
Algebraic methods in functional analysis: the Victor Shulman anniversary volume. ed. / Ivan G. Todorov; Lyudmila Turowska. Basel: Springer Verlag, 2014. p. 33-44 (Operator Theory: Advances and Applications; Vol. 233).

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSNChapter

Harvard

Choi, Y 2014, Singly generated operator algebras satisfying weakened versions of amenability. in IG Todorov & L Turowska (eds), Algebraic methods in functional analysis: the Victor Shulman anniversary volume. Operator Theory: Advances and Applications, vol. 233, Springer Verlag, Basel, pp. 33-44. https://doi.org/10.1007/978-3-0348-0502-5_3

APA

Choi, Y. (2014). Singly generated operator algebras satisfying weakened versions of amenability. In I. G. Todorov, & L. Turowska (Eds.), Algebraic methods in functional analysis: the Victor Shulman anniversary volume (pp. 33-44). (Operator Theory: Advances and Applications; Vol. 233). Springer Verlag. https://doi.org/10.1007/978-3-0348-0502-5_3

Vancouver

Choi Y. Singly generated operator algebras satisfying weakened versions of amenability. In Todorov IG, Turowska L, editors, Algebraic methods in functional analysis: the Victor Shulman anniversary volume. Basel: Springer Verlag. 2014. p. 33-44. (Operator Theory: Advances and Applications). doi: 10.1007/978-3-0348-0502-5_3

Author

Choi, Yemon. / Singly generated operator algebras satisfying weakened versions of amenability. Algebraic methods in functional analysis: the Victor Shulman anniversary volume. editor / Ivan G. Todorov ; Lyudmila Turowska. Basel : Springer Verlag, 2014. pp. 33-44 (Operator Theory: Advances and Applications).

Bibtex

@inbook{859eca9771214102b85b68dc4889780a,
title = "Singly generated operator algebras satisfying weakened versions of amenability",
abstract = "We construct a singly generated subalgebra of K(H) which is nonamenable, yet is boundedly approximately contractible. The example embeds into a homogeneous von Neumann algebra. We also observe that there are singly generated, biflat subalgebras of finite Type I von Neumann algebras, which are not amenable (and hence are not isomorphic to C*-algebras). Such an example can be used to show that a certain extension property for commutative operator algebras, which is shown in [3] to follow from amenability, does not necessarily imply amenability.",
keywords = "Approximate amenability , biflatness , compact operators , finite von Neumann algebra , monogenic Banach algebra , Type I von Neumann algebra",
author = "Yemon Choi",
year = "2014",
doi = "10.1007/978-3-0348-0502-5_3",
language = "English",
isbn = "9783034805018",
series = "Operator Theory: Advances and Applications",
publisher = "Springer Verlag",
pages = "33--44",
editor = "Todorov, {Ivan G.} and Lyudmila Turowska",
booktitle = "Algebraic methods in functional analysis",

}

RIS

TY - CHAP

T1 - Singly generated operator algebras satisfying weakened versions of amenability

AU - Choi, Yemon

PY - 2014

Y1 - 2014

N2 - We construct a singly generated subalgebra of K(H) which is nonamenable, yet is boundedly approximately contractible. The example embeds into a homogeneous von Neumann algebra. We also observe that there are singly generated, biflat subalgebras of finite Type I von Neumann algebras, which are not amenable (and hence are not isomorphic to C*-algebras). Such an example can be used to show that a certain extension property for commutative operator algebras, which is shown in [3] to follow from amenability, does not necessarily imply amenability.

AB - We construct a singly generated subalgebra of K(H) which is nonamenable, yet is boundedly approximately contractible. The example embeds into a homogeneous von Neumann algebra. We also observe that there are singly generated, biflat subalgebras of finite Type I von Neumann algebras, which are not amenable (and hence are not isomorphic to C*-algebras). Such an example can be used to show that a certain extension property for commutative operator algebras, which is shown in [3] to follow from amenability, does not necessarily imply amenability.

KW - Approximate amenability

KW - biflatness

KW - compact operators

KW - finite von Neumann algebra

KW - monogenic Banach algebra

KW - Type I von Neumann algebra

U2 - 10.1007/978-3-0348-0502-5_3

DO - 10.1007/978-3-0348-0502-5_3

M3 - Chapter

SN - 9783034805018

T3 - Operator Theory: Advances and Applications

SP - 33

EP - 44

BT - Algebraic methods in functional analysis

A2 - Todorov, Ivan G.

A2 - Turowska, Lyudmila

PB - Springer Verlag

CY - Basel

ER -