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UNBOUNDED DERIVATIONS IN ALGEBRAS ASSOCIATED WITH MONOTHETIC GROUPS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  13 January 2020

SLAWOMIR KLIMEK  and
MATT McBRIDE
SLAWOMIR KLIMEK
Affiliation:
Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN 46202, USA e-mail: [email protected]
MATT McBRIDE*
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, 175 President’s Cir., Mississippi State, MS 39762, USA
*
e-mail: [email protected]
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Abstract

Given an infinite, compact, monothetic group $G$ we study decompositions and structure of unbounded derivations in a crossed product $\text{C}^{\ast }$-algebra $C(G)\rtimes \mathbb{Z}$ obtained from a translation on $G$ by a generator of a dense cyclic subgroup. We also study derivations in a Toeplitz extension of the crossed product and the question whether unbounded derivations can be lifted from one algebra to the other.

Keywords

derivationsoperator algebraMonothetic groups

MSC classification

Primary: 46L52: Noncommutative function spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 111 , Issue 3 , December 2021 , pp. 345 - 371
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by L. O. Clark

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