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Cover: 9781441924797 | A Course in Commutative Banach Algebras | Eberhard Kaniuth | Buch
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A Course in Commutative Banach Algebras
Taschenbuch von Eberhard Kaniuth
Sprache: Englisch

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Beschreibung
Banach algebras are Banach spaces equipped with a continuous multipli- tion. In roughterms,there arethree types ofthem:algebrasofboundedlinear operators on Banach spaces with composition and the operator norm, al- bras consisting of bounded continuous functions on topological spaces with pointwise product and the uniform norm, and algebrasof integrable functions on locally compact groups with convolution as multiplication. These all play a key role in modern analysis. Much of operator theory is best approached from a Banach algebra point of view and many questions in complex analysis (such as approximation by polynomials or rational functions in speci?c - mains) are best understood within the framework of Banach algebras. Also, the study of a locally compact Abelian group is closely related to the study 1 of the group algebra L (G). There exist a rich literature and excellent texts on each single class of Banach algebras, notably on uniform algebras and on operator algebras. This work is intended as a textbook which provides a thorough introduction to the theory of commutative Banach algebras and stresses the applications to commutative harmonic analysis while also touching on uniform algebras. In this sense and purpose the book resembles Larsen¿s classical text [75] which shares many themes and has been a valuable resource. However, for advanced graduate students and researchers I have covered several topics which have not been published in books before, including some journal articles.
Banach algebras are Banach spaces equipped with a continuous multipli- tion. In roughterms,there arethree types ofthem:algebrasofboundedlinear operators on Banach spaces with composition and the operator norm, al- bras consisting of bounded continuous functions on topological spaces with pointwise product and the uniform norm, and algebrasof integrable functions on locally compact groups with convolution as multiplication. These all play a key role in modern analysis. Much of operator theory is best approached from a Banach algebra point of view and many questions in complex analysis (such as approximation by polynomials or rational functions in speci?c - mains) are best understood within the framework of Banach algebras. Also, the study of a locally compact Abelian group is closely related to the study 1 of the group algebra L (G). There exist a rich literature and excellent texts on each single class of Banach algebras, notably on uniform algebras and on operator algebras. This work is intended as a textbook which provides a thorough introduction to the theory of commutative Banach algebras and stresses the applications to commutative harmonic analysis while also touching on uniform algebras. In this sense and purpose the book resembles Larsen¿s classical text [75] which shares many themes and has been a valuable resource. However, for advanced graduate students and researchers I have covered several topics which have not been published in books before, including some journal articles.
Zusammenfassung

This book provides a thorough and self-contained introduction to the theory of commutative Banach algebras. The author has carefully chosen the most important topics within Banach algebra theory. At the core of this text are the chapters on Gelfand's theory, regularity and spectral synthesis. Special emphasis is placed on applications in abstract harmonic analysis and on treating many special classes of commutative Banach algebras, such as uniform algebras, group algebras and Beurling algebras, and tensor products. Detailed proofs and a variety of exercises are given. The book is intended for graduate students taking a course on Banach algebras, with various possible specializations, or a Gelfand theory based course in harmonic analysis.

Inhaltsverzeichnis
General Theory of Banach Algebras.- Gelfand Theory.- Functional Calculus, Shilov Boundary, and Applications.- Regularity and Related Properties.- Spectral Synthesis and Ideal Theory.
Details
Erscheinungsjahr: 2010
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Graduate Texts in Mathematics
Inhalt: xii
353 S.
ISBN-13: 9781441924797
ISBN-10: 1441924795
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Kaniuth, Eberhard
Auflage: Softcover reprint of hardcover 1st ed. 2009
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 235 x 155 x 20 mm
Von/Mit: Eberhard Kaniuth
Erscheinungsdatum: 19.11.2010
Gewicht: 0,557 kg
Artikel-ID: 107152533
Zusammenfassung

This book provides a thorough and self-contained introduction to the theory of commutative Banach algebras. The author has carefully chosen the most important topics within Banach algebra theory. At the core of this text are the chapters on Gelfand's theory, regularity and spectral synthesis. Special emphasis is placed on applications in abstract harmonic analysis and on treating many special classes of commutative Banach algebras, such as uniform algebras, group algebras and Beurling algebras, and tensor products. Detailed proofs and a variety of exercises are given. The book is intended for graduate students taking a course on Banach algebras, with various possible specializations, or a Gelfand theory based course in harmonic analysis.

Inhaltsverzeichnis
General Theory of Banach Algebras.- Gelfand Theory.- Functional Calculus, Shilov Boundary, and Applications.- Regularity and Related Properties.- Spectral Synthesis and Ideal Theory.
Details
Erscheinungsjahr: 2010
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Graduate Texts in Mathematics
Inhalt: xii
353 S.
ISBN-13: 9781441924797
ISBN-10: 1441924795
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Kaniuth, Eberhard
Auflage: Softcover reprint of hardcover 1st ed. 2009
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 235 x 155 x 20 mm
Von/Mit: Eberhard Kaniuth
Erscheinungsdatum: 19.11.2010
Gewicht: 0,557 kg
Artikel-ID: 107152533
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