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Other titles in the Universitext series:
NonCommutative Gelfand Theories: A ToolKit for Operator Theorists and Numerical Analysts (Universitext)by Steffen Roch
Synopses & ReviewsPublisher Comments:<p>Written as a hybrid between a research monograph and a textbook the first half of this book is concerned with basic concepts for the study of Banach algebras that, in a sense, are not too far from being commutative. Essentially, the algebra under consideration either has a sufficiently large center or is subject to a higher order commutator property (an algebra with a socalled polynomial identity or in short: Plalgebra). In the second half of the book, a number of selected examples are used to demonstrate how this theory can be successfully applied to problems in operator theory and numerical analysis.</p> <p>Distinguished by the consequent use of local principles (noncommutative Gelfand theories), PIalgebras, Mellin techniques and limit operator techniques, each one of the applications presented in chapters 4, 5 and 6 forms a theory that is up to modern standards and interesting in its own right.</p> <p>Written in a way that can be worked through by the reader with fundamental knowledge of analysis, functional analysis and algebra, this book will be accessible to 4th year students of mathematics or physics whilst also being of interest to researchers in the areas of operator theory, numerical analysis, and the general theory of Banach algebras.</p>
Synopsis:This book offers basic concepts for the study of Banach algebras that, in a sense, are not far from being commutative. Includes selected examples to demonstrate how this theory can be successfully applied to problems in operator theory and numerical analysis.
Synopsis:Written as a hybrid between a research monograph and a textbook the first half of this book is concerned with basic concepts for the study of Banach algebras that, in a sense, are not too far from being commutative. Essentially, the algebra under consideration either has a sufficiently large center or is subject to a higher order commutator property (an algebra with a socalled polynomial identity or in short: Plalgebra). In the second half of the book, a number of selected examples are used to demonstrate how this theory can be successfully applied to problems in operator theory and numerical analysis. Distinguished by the consequent use of local principles (noncommutative Gelfand theories), PIalgebras, Mellin techniques and limit operator techniques, each one of the applications presented in chapters 4, 5 and 6 forms a theory that is up to modern standards and interesting in its own right. Written in a way that can be worked through by the reader with fundamental knowledge of analysis, functional analysis and algebra, this book will be accessible to 4th year students of mathematics or physics whilst also being of interest to researchers in the areas of operator theory, numerical analysis, and the general theory of Banach algebras.
Table of ContentsBanach algebras. Local principles. Banach algebras generated by idempotents. Singular integral operators. Convolution operators. Algebras of operator sequences.
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