Spectral Mapping Theorems
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Spectral Mapping Theorems
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Author : Robin Harte
language : en
Publisher: Springer Nature
Release Date : 2023-04-03
Spectral Mapping Theorems written by Robin Harte and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-03 with Mathematics categories.
Written by an author who was at the forefront of developments in multivariable spectral theory during the seventies and the eighties, this book describes the spectral mapping theorem in various settings. In this second edition, the Bluffer's Guide has been revised and expanded, whilst preserving the engaging style of the first. Starting with a summary of the basic algebraic systems – semigroups, rings and linear algebras – the book quickly turns to topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Key aspects of spectral theory are covered, in one and several variables. Finally the case of an arbitrary set of variables is discussed. Spectral Mapping Theorems is an accessible and easy-to-read guide, providing a convenient overview of the topic to both students and researchers. From the reviews of the first edition "I certainly plan to add it to my own mathematical library" — Anthony Wickstead in the Irish Mathematical Society Bulletin "An excellent read" — Milena Stanislavova in the Mathematical Reviews "[Offers] a fresh perspective even for experts [...] Recommended" — David Feldman in Choice
Spectral Mapping Theorems
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Author : R. E. Harte
language : en
Publisher:
Release Date : 1972
Spectral Mapping Theorems written by R. E. Harte and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
Spectral Mapping Theorems
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Author : Robin Harte
language : en
Publisher: Springer
Release Date : 2014-04-29
Spectral Mapping Theorems written by Robin Harte and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-29 with Mathematics categories.
Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several and many variables. The basic algebraic systems – semigroups, rings and linear algebras – are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Spectral Mapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory.
Spectral Mapping Theorems For Subnormal Operators
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Author : James Joseph Dudziak
language : en
Publisher:
Release Date : 1983
Spectral Mapping Theorems For Subnormal Operators written by James Joseph Dudziak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mappings (Mathematics) categories.
Fredholm And Local Spectral Theory With Applications To Multipliers
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Author : Pietro Aiena
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-08
Fredholm And Local Spectral Theory With Applications To Multipliers written by Pietro Aiena and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-08 with Mathematics categories.
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.
Spectral Theory Of Linear Operators And Spectral Systems In Banach Algebras
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Author : Vladimir Müller
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Spectral Theory Of Linear Operators And Spectral Systems In Banach Algebras written by Vladimir Müller and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
Spectral theory is an important part of functional analysis.It has numerous appli cations in many parts of mathematics and physics including matrix theory, func tion theory, complex analysis, differential and integral equations, control theory and quantum physics. In recent years, spectral theory has witnessed an explosive development. There are many types of spectra, both for one or several commuting operators, with important applications, for example the approximate point spectrum, Taylor spectrum, local spectrum, essential spectrum, etc. The present monograph is an attempt to organize the available material most of which exists only in the form of research papers scattered throughout the literature. The aim is to present a survey of results concerning various types of spectra in a unified, axiomatic way. The central unifying notion is that of a regularity, which in a Banach algebra is a subset of elements that are considered to be "nice". A regularity R in a Banach algebra A defines the corresponding spectrum aR(a) = {A E C : a - ,\ rJ. R} in the same way as the ordinary spectrum is defined by means of invertible elements, a(a) = {A E C : a - ,\ rJ. Inv(A)}. Axioms of a regularity are chosen in such a way that there are many natural interesting classes satisfying them. At the same time they are strong enough for non-trivial consequences, for example the spectral mapping theorem.
Trotter Kato Product Formul
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Author : Valentin A. Zagrebnov
language : en
Publisher: Springer Nature
Release Date : 2024-06-11
Trotter Kato Product Formul written by Valentin A. Zagrebnov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-11 with Mathematics categories.
The book captures a fascinating snapshot of the current state of results about the operator-norm convergent Trotter-Kato Product Formulæ on Hilbert and Banach spaces. It also includes results on the operator-norm convergent product formulæ for solution operators of the non-autonomous Cauchy problems as well as similar results on the unitary and Zeno product formulæ. After the Sophus Lie product formula for matrices was established in 1875, it was generalised to Hilbert and Banach spaces for convergence in the strong operator topology by H. Trotter (1959) and then in an extended form by T. Kato (1978). In 1993 Dzh. L. Rogava discovered that convergence of the Trotter product formula takes place in the operator-norm topology. The latter is the main subject of this book, which is dedicated essentially to the operator-norm convergent Trotter-Kato Product Formulæ on Hilbert and Banach spaces, but also to related results on the time-dependent, unitary and Zeno product formulæ. The book yields a detailed up-to-date introduction into the subject that will appeal to any reader with a basic knowledge of functional analysis and operator theory. It also provides references to the rich literature and historical remarks.
Fredholm And Local Spectral Theory Ii
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Author : Pietro Aiena
language : en
Publisher: Springer
Release Date : 2018-11-24
Fredholm And Local Spectral Theory Ii written by Pietro Aiena and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-24 with Mathematics categories.
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.
Spectral Theory Of Bounded Linear Operators
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Author : Carlos S. Kubrusly
language : en
Publisher: Springer Nature
Release Date : 2020-01-30
Spectral Theory Of Bounded Linear Operators written by Carlos S. Kubrusly and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-30 with Mathematics categories.
This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and (iii) the Fredholm theory in both Banach and Hilbert spaces. Detailed proofs of all theorems are included and presented with precision and clarity, especially for the spectral theorems, allowing students to thoroughly familiarize themselves with all the important concepts. Covering both basic and more advanced material, the five chapters and two appendices of this volume provide a modern treatment on spectral theory. Topics range from spectral results on the Banach algebra of bounded linear operators acting on Banach spaces to functional calculus for Hilbert and Banach-space operators, including Fredholm and multiplicity theories. Supplementary propositions and further notes are included as well, ensuring a wide range of topics in spectral theory are covered. Spectral Theory of Bounded Linear Operators is ideal for graduate students in mathematics, and will also appeal to a wider audience of statisticians, engineers, and physicists. Though it is mostly self-contained, a familiarity with functional analysis, especially operator theory, will be helpful.