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Weighted Hardy Spaces Over the Unit Ball: The Freely Noncommutative and Commutative Settings Read chapter Read first chapter

2024 | OriginalPaper | Chapter

Geometric Structures Related to a \(W^*\)-Algebra

Author : Aneta Sliżewska

Published in: Operator and Matrix Theory, Function Spaces, and Applications

Publisher: Springer Nature Switzerland

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Abstract

In this presentation we will show that the groupoid of partially invertible elements and, in particular, the groupoid of partial isometries of a \(W^*\)-algebra, have the structure of Banach- Lie groupoids. The relationship between these groupoids, their algebroids and the Banach-Poisson geometry will also be shown.

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previous chapter On Abstract Spectral Constants
next chapter Composition in Reproducing Kernel Hilbert Spaces à Rebours
Appendix
Available only for authorised users
Literature
1.
A. Cannas da Silva, A. Weinstein, Geometric Models for Noncommutative Algebras (AMS Bookstore, Providence, 1999)
2.
K. Mackenzie. General Theory of Lie Groupoids and Lie Algebroids (Cambridge University Press, Cambridge, 2005)CrossRef
3.
K. Mackenzie, A. Odzijewicz, A Sliżewska, Poisson geometry related to Atiyah sequences. Symmetry Integr. Geom. Methods Appl. 14, 1–29 (2018)
4.
5.
A. Odzijewicz, A. Sliżewska, Banach-Lie groupoids associated to \(W^*\)-algebras. J. Symplectic Geom. 14(3), 687–736 (2016)
6.
A. Odzijewicz, G. Jakimowicz, A. Sliżewska, Banach-Lie algebroids associated to the groupoid of partially invertible elements of a \(W^*\)-algebra. J. Geom. Phys. 95, 108–126 (2015)
7.
A. Odzijewicz, G. Jakimowicz, A. Sliżewska, Fibre-wise linear Poisson structures related to \(W^*\)-algebras. J. Geom. Phys. 123, 385–423 (2018)
8.
S. Sakai, \(C^*\)-algebras and\(W^*\)-algebras (Springer-Verlag, Berlin, 1971)
Metadata
Title
Geometric Structures Related to a -Algebra
Author
Aneta Sliżewska
Copyright Year
2024
Book
Operator and Matrix Theory, Function Spaces, and Applications

Print ISBN: 978-3-031-50612-3

Electronic ISBN: 978-3-031-50613-0

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-50613-0_16

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