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.
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