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ON POSSIBLE VALUES OF THE INTERIOR ANGLE BETWEEN INTERMEDIATE SUBALGEBRAS

Part of: Linear spaces and algebras of operators Selfadjoint operator algebras

Published online by Cambridge University Press:  17 July 2023

VED PRAKASH GUPTA Open the ORCID record for VED PRAKASH GUPTA [Opens in a new window]  and
DEEPIKA SHARMA
VED PRAKASH GUPTA
Affiliation:
School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India e-mail: vedgupta@mail.jnu.ac.in
DEEPIKA SHARMA*
Affiliation:
School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India
*
e-mail: sharmadeepikaq@gmail.com
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Abstract

We show that all values in the interval $[0,{\pi }/{2}]$ can be attained as interior angles between intermediate subalgebras (as introduced by Bakshi and the first named author [‘Lattice of intermediate subalgebras’, J. Lond. Math. Soc. (2) 104(2) (2021), 2082–2127]) of a certain inclusion of simple unital $C^*$-algebras. We also calculate the interior angles between intermediate crossed product subalgebras of any inclusion of crossed product algebras corresponding to any action of a countable discrete group and its subgroups on a unital $C^*$-algebra.

Keywords

intermediate subalgebrasinterior anglecrossed productsgroup C*-algebrasinclusions of C*-algebrassimple C*-algebrasfinite-index conditional expectationsC*-basic construction

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 47L40: Limit algebras, subalgebras of $C^*$-algebras

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 117 , Issue 1 , August 2024 , pp. 44 - 66
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by Aidan Sims

References

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