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.
Representations of *-Algebras, Locally Compact Groups, an...
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Editorial Reviews
Review
The authors have succeeded admirably, and these two volumes are a pleasure to read as well as being a valuable reference.
[It] contains a valuable explanation of the relationship between representation theory and physics which every mathematician should be made aware of.
--MATHEMATICAL REVIEWS
There are many helpful remarks and asides throughout the text as well as extensive exercises and historical discussions at the end of each chapter. These two volumes are a valuable addition to anyone's library as well as a pleasurable avenue to representation theory.
--MATHEMATICAL REVIEW
The work is a most authoritative account of representation theory and Mackey's theory; it will no doubt become the standard work of references in thefield for years to come.
--MONATSHEFTE FUR MATHEMATIK
These volumes have been prepared with great care. The exposition is clear and thorough.
--AMERICAN MATHEMATICAL MONTHLY
[It] contains a valuable explanation of the relationship between representation theory and physics which every mathematician should be made aware of.
--MATHEMATICAL REVIEWS
There are many helpful remarks and asides throughout the text as well as extensive exercises and historical discussions at the end of each chapter. These two volumes are a valuable addition to anyone's library as well as a pleasurable avenue to representation theory.
--MATHEMATICAL REVIEW
The work is a most authoritative account of representation theory and Mackey's theory; it will no doubt become the standard work of references in thefield for years to come.
--MONATSHEFTE FUR MATHEMATIK
These volumes have been prepared with great care. The exposition is clear and thorough.
--AMERICAN MATHEMATICAL MONTHLY
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Inside This Book
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First Sentence:
The main purpose of the present Volume 2 is to give a detailed presentation of the Mackey "normal subgroup analysis" for classifying the unitary representations of groups-and this not merely in the customary context of locally compact groups, but in the larger context of Banach -algebraic bundles. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
normal subgroup analysis, strong approximate unit, locally convex representations, imprimitivity theorem, imprimitivity bimodule, unitary multipliers, dense contraction, rigged modules, conjugating action, fiber algebra, involutory context, whose integrated form, regional topology, regional topologies, cocycle bundle, saturated bundles, projective representation theory, bundle retraction, twisted group algebras, commuting algebras, operator inner product, algebraic bundle, direct product extension, inducing operation, dense linear span Key Phrases - Capitalized Phrases (CAPs): (learn more)
Frobenius Reciprocity Theorem, Peter-Weyl Theorem, Stone-Weierstrass Theorem, B-rigged A-module, Fubini's Theorem, Pontryagin Duality Theorem, Unit Fibers of Compact Type, Stone's Theorem, X-projection-valued Borel, Schwarz Inequality, Fubini Theorem, Hermitian A-module, Schwarz's Inequality, Stone-von Neumann Theorem, Philip Green, The Existence of Irreducible, Wendel's Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
The main purpose of the present Volume 2 is to give a detailed presentation of the Mackey "normal subgroup analysis" for classifying the unitary representations of groups-and this not merely in the customary context of locally compact groups, but in the larger context of Banach -algebraic bundles. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
normal subgroup analysis, strong approximate unit, locally convex representations, imprimitivity theorem, imprimitivity bimodule, unitary multipliers, dense contraction, rigged modules, conjugating action, fiber algebra, involutory context, whose integrated form, regional topology, regional topologies, cocycle bundle, saturated bundles, projective representation theory, bundle retraction, twisted group algebras, commuting algebras, operator inner product, algebraic bundle, direct product extension, inducing operation, dense linear span Key Phrases - Capitalized Phrases (CAPs): (learn more)
Frobenius Reciprocity Theorem, Peter-Weyl Theorem, Stone-Weierstrass Theorem, B-rigged A-module, Fubini's Theorem, Pontryagin Duality Theorem, Unit Fibers of Compact Type, Stone's Theorem, X-projection-valued Borel, Schwarz Inequality, Fubini Theorem, Hermitian A-module, Schwarz's Inequality, Stone-von Neumann Theorem, Philip Green, The Existence of Irreducible, Wendel's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 66
books:
See all 66 books this book cites
- An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics) by William M. Boothby in Back Matter (1), and Back Matter (2)
- A First Course in Rational Continuum Mechanics (Pure and applied mathematics, a series of monographs and textbooks) by Clifford A. Truesdell in Back Matter
- Positive Operators by Charalambos D. Aliprantis in Back Matter
- Number theory, Volume 20 (Pure and Applied Mathematics) by Author Unknown in Back Matter
- Differential algebraic groups, Volume 114 (Pure and Applied Mathematics) by Author Unknown in Back Matter
See all 66 books this book cites
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