Group representations in Banach spaces and Banach lattices

Leiden Repository

Group representations in Banach spaces and Banach lattices

Title: Group representations in Banach spaces and Banach lattices
Author: Wortel, Marten Rogier
Publisher: Mathematical Institute, Faculty of Science, Leiden University
Issue Date: 2012-04-18
Keywords: Banach algebra crossed product
Banach lattice
Positive group representation.
Abstract: In this thesis, group representations in Banach spaces and Banach lattices are studied. In the first part, chapter 2, a Banach algebra crossed product is constructed, which is an object that allows the translation of group representations in Banach spaces into Banach algebra representations. This can be used to understand these group representations, provided that these Banach algebra representations are sufficiently well understood. In the second part, positive group representations on Riesz spaces are studied. In chapter 3, the theory of such representations of finite groups is studied, mainly in finite dimensional spaces. The main results are that irreducible positive representations of finite groups on sufficiently nice Riesz spaces are finite dimensional, and the finite dimensional positive representations are equal to permutation representations conjugated by a diagonal matrix. In chapter 4 this is taken to the next level by considering positive representations of compact groups on Banach lattices. It turns out that these representations are often equal to an isometric positive representation conjugated by a central lattice automorphism.
Description: Promotor: S.M. Verduyn Lunel, Co-promotores: M.F.E. de Jeu, B. de Pagter
With summary in Dutch
Faculty: Faculteit der Wiskunde en Natuurwetenschappen
Citation: Wortel, M.R., 2012, Doctoral thesis, Leiden University
ISBN: 9789461912404

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application/pdf Chapter 1 Introduction 297.6Kb View/Open
application/pdf Chapter 2 620.9Kb View/Open
application/pdf Chapter 3 429.9Kb View/Open
application/pdf Chapter 4 399.5Kb View/Open
application/pdf Bibliography_Acknowledgements 219.3Kb View/Open
application/pdf Summary in Dutch 192.0Kb View/Open
application/pdf Curriculum Vitae 123.6Kb View/Open
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