TY  - BOOK
AU  - Roch,Steffen
AU  - Santos,Pedro A.
AU  - Silbermann,Bernd
ED  - SpringerLink (Online service)
TI  - Non-commutative Gelfand Theories: A Tool-kit for Operator Theorists and Numerical Analysts 
T2  - Universitext
SN  - 9780857291837
AV  - QA319-329.9 
U1  - 515.7 23
PY  - 2011///
CY  - London
PB  - Springer London
KW  - Mathematics
KW  - Fourier analysis
KW  - Functional analysis
KW  - Integral equations
KW  - Operator theory
KW  - Numerical analysis
KW  - Functional Analysis
KW  - Numerical Analysis
KW  - Integral Equations
KW  - Operator Theory
KW  - Fourier Analysis
N1  - Banach algebras -- Local principles -- Banach algebras generated by idempotents -- Singular integral operators -- Convolution operators -- Algebras of operator sequences
N2  - 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 so-called polynomial identity or in short: Pl-algebra). 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 (non-commutative Gelfand theories), PI-algebras, 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
UR  - http://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-0-85729-183-7
ER  -