Banach Algebraic Bundles Induced Representations And The Generalized Mackey Analysis
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Author | : J. M.G. Fell |
Publisher | : Academic Press |
Total Pages | : 755 |
Release | : 1988-05-01 |
Genre | : Mathematics |
ISBN | : 0080874452 |
This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.
Author | : James Michael Gardner Fell |
Publisher | : |
Total Pages | : 740 |
Release | : 1988 |
Genre | : |
ISBN | : |
Author | : J. M.G. Fell |
Publisher | : Academic Press |
Total Pages | : 746 |
Release | : 1988-04-11 |
Genre | : Mathematics |
ISBN | : 9780122527210 |
This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.
Author | : James Michael Gardner Fell |
Publisher | : |
Total Pages | : 8 |
Release | : 1988 |
Genre | : Banach algebras |
ISBN | : |
Author | : James Michael Gardner Fell |
Publisher | : American Mathematical Soc. |
Total Pages | : 172 |
Release | : 1969 |
Genre | : Banach algebras |
ISBN | : 0821812904 |
The main object of the present memoir is to show that the methods and results of Mackey (1958) and Blattner (1963) on the group extension representation problem go through without any essential change in the larger context of homogeneous Banach *-algebraic bundles (with enough cross sections). In order to dispense with separability we shall follow the topological methods of Blattner rather than Mackey's more detailed measure-theoretic analysis. Except for the last section, Part II of this memoir is in fact a rewriting of much of Blattner's papers (1963), making the modifications necessary in the larger context of bundles. The last Section 17 gives an account of the 'Mackey obstruction' in the nonseparable case, leading to an analogue (Theorem 17.2) of Theorem 8.2 of Mackey's paper for homogeneous Banach *-algebraic bundles, without separability restrictions. This is the culminating point of the present memoir.
Author | : J. M. G. Fell |
Publisher | : Springer |
Total Pages | : 354 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540699775 |
Author | : Eberhard Kaniuth |
Publisher | : Cambridge University Press |
Total Pages | : 359 |
Release | : 2013 |
Genre | : Mathematics |
ISBN | : 052176226X |
A comprehensive presentation of the theories of induced representations and Mackey analysis applied to a wide variety of groups.
Author | : Robert S. Doran |
Publisher | : American Mathematical Soc. |
Total Pages | : 458 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821842250 |
George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics.
Author | : Dana P. Williams |
Publisher | : American Mathematical Soc. |
Total Pages | : 546 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821842420 |
The theory of crossed products is extremely rich and intriguing. There are applications not only to operator algebras, but to subjects as varied as noncommutative geometry and mathematical physics. This book provides a detailed introduction to this vast subject suitable for graduate students and others whose research has contact with crossed product $C*$-algebras. in addition to providing the basic definitions and results, the main focus of this book is the fine ideal structure of crossed products as revealed by the study of induced representations via the Green-Mackey-Rieffel machine. in particular, there is an in-depth analysis of the imprimitivity theorems on which Rieffel's theory of induced representations and Morita equivalence of $C*$-algebras are based. There is also a detailed treatment of the generalized Effros-Hahn conjecture and its proof due to Gootman, Rosenberg, and Sauvageot. This book is meant to be self-contained and accessible to any graduate student coming out of a first course on operator algebras. There are appendices that deal with ancillary subjects, which while not central to the subject, are nevertheless crucial for a complete understanding of the material. Some of the appendices will be of independent interest. to view another book by this author, please visit Morita Equivalence and Continuous-Trace $C*$-Algebras.
Author | : Tullio Ceccherini-Silberstein |
Publisher | : Springer Nature |
Total Pages | : 153 |
Release | : 2020-09-25 |
Genre | : Mathematics |
ISBN | : 3030516075 |
This monograph is the first comprehensive treatment of multiplicity-free induced representations of finite groups as a generalization of finite Gelfand pairs. Up to now, researchers have been somehow reluctant to face such a problem in a general situation, and only partial results were obtained in the one-dimensional case. Here, for the first time, new interesting and important results are proved. In particular, after developing a general theory (including the study of the associated Hecke algebras and the harmonic analysis of the corresponding spherical functions), two completely new highly nontrivial and significant examples (in the setting of linear groups over finite fields) are examined in full detail. The readership ranges from graduate students to experienced researchers in Representation Theory and Harmonic Analysis.