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This monograph concerns the relationship between the local spectral
theory and Fredholm theory of bounded linear operators acting on
Banach spaces. The purpose of this book is to provide a first
general treatment of the theory of operators for which Weyl-type or
Browder-type theorems hold. The product of intensive research
carried out over the last ten years, this book explores for the
first time in a monograph form, results that were only previously
available in journal papers. Written in a simple style, with
sections and chapters following an easy, natural flow, it will be
an invaluable resource for researchers in Operator Theory and
Functional Analysis. The reader is assumed to be familiar with the
basic notions of linear algebra, functional analysis and complex
analysis.
A signi?cant sector of the development of spectral theory outside
the classical area of Hilbert space may be found amongst at
multipliers de?ned on a complex commutative Banach algebra A.
Although the general theory of multipliers for abstract Banach
algebras has been widely investigated by several authors, it is
surprising how rarely various aspects of the spectral theory, for
instance Fredholm theory and Riesz theory, of these important
classes of operators have been studied. This scarce consideration
is even more surprising when one observes that the various aspects
of spectral t- ory mentioned above are quite similar to those of a
normal operator de?ned on a complex Hilbert space. In the last ten
years the knowledge of the spectral properties of multip- ers of
Banach algebras has increased considerably, thanks to the
researches undertaken by many people working in local spectral
theory and Fredholm theory. This research activity recently
culminated with the publication of the book of Laursen and Neumann
[214], which collects almost every thing that is known about the
spectral theory of multipliers.
A signi?cant sector of the development of spectral theory outside
the classical area of Hilbert space may be found amongst at
multipliers de?ned on a complex commutative Banach algebra A.
Although the general theory of multipliers for abstract Banach
algebras has been widely investigated by several authors, it is
surprising how rarely various aspects of the spectral theory, for
instance Fredholm theory and Riesz theory, of these important
classes of operators have been studied. This scarce consideration
is even more surprising when one observes that the various aspects
of spectral t- ory mentioned above are quite similar to those of a
normal operator de?ned on a complex Hilbert space. In the last ten
years the knowledge of the spectral properties of multip- ers of
Banach algebras has increased considerably, thanks to the
researches undertaken by many people working in local spectral
theory and Fredholm theory. This research activity recently
culminated with the publication of the book of Laursen and Neumann
[214], which collects almost every thing that is known about the
spectral theory of multipliers.
Based on lectures given at an instructional course, this volume enables readers with a basic knowledge of functional analysis to access key research in the field. The authors survey several areas of current interest, making this volume ideal preparatory reading for students embarking on graduate work as well as for mathematicians working in related areas.
Based on lectures given at an instructional course, this volume enables readers with a basic knowledge of functional analysis to access key research in the field. The authors survey several areas of current interest, making this volume ideal preparatory reading for students embarking on graduate work as well as for mathematicians working in related areas.
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