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Author : Anthony Francis Ruston
Publisher : Cambridge University Press
Page : 314 pages
File Size : 44,8 Mb
Release : 2004-06-03
Category : Mathematics
ISBN : 0521604931
Presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind.
Author : Pietro Aiena
Publisher : Springer
Page : 546 pages
File Size : 53,9 Mb
Release : 2018-11-24
Category : Mathematics
ISBN : 9783030022662
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.
Author : Pietro Aiena
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 48,5 Mb
Release : 2007-05-08
Category : Mathematics
ISBN : 9781402025259
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.
Author : C.-G. Ambrozie,Florian-Horia Vasilescu
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401103756
The aim of this work is to initiate a systematic study of those properties of Banach space complexes that are stable under certain perturbations. A Banach space complex is essentially an object of the form 1 op-l oP +1 ... --+ XP- --+ XP --+ XP --+ ... , where p runs a finite or infiniteinterval ofintegers, XP are Banach spaces, and oP : Xp ..... Xp+1 are continuous linear operators such that OPOp-1 = 0 for all indices p. In particular, every continuous linear operator S : X ..... Y, where X, Yare Banach spaces, may be regarded as a complex: O ..... X ~ Y ..... O. The already existing Fredholm theory for linear operators suggested the possibility to extend its concepts and methods to the study of Banach space complexes. The basic stability properties valid for (semi-) Fredholm operators have their counterparts in the more general context of Banach space complexes. We have in mind especially the stability of the index (i.e., the extended Euler characteristic) under small or compact perturbations, but other related stability results can also be successfully extended. Banach (or Hilbert) space complexes have penetrated the functional analysis from at least two apparently disjoint directions. A first direction is related to the multivariable spectral theory in the sense of J. L.
Author : Bruce A. Barnes
Publisher : Pitman Publishing
Page : 144 pages
File Size : 51,5 Mb
Release : 1982
Category : Mathematics
ISBN : UCAL:B2504857
Author : Robert E. Megginson
Publisher : Springer Science & Business Media
Page : 636 pages
File Size : 46,7 Mb
Release : 1998-10-09
Category : Mathematics
ISBN : 0387984313
This book is an introduction to the general theory of Banach spaces, designed to prepare the reader with a background in functional analysis that will enable him or her to tackle more advanced literature in the subject. The book is replete with examples, historical notes, and citations, as well as nearly 500 exercises.
Author : Helmut Hofer,Krzysztof Wysocki,Eduard Zehnder
Publisher : Springer Nature
Page : 1001 pages
File Size : 49,5 Mb
Release : 2021-07-21
Category : Mathematics
ISBN : 9783030780074
This book pioneers a nonlinear Fredholm theory in a general class of spaces called polyfolds. The theory generalizes certain aspects of nonlinear analysis and differential geometry, and combines them with a pinch of category theory to incorporate local symmetries. On the differential geometrical side, the book introduces a large class of `smooth’ spaces and bundles which can have locally varying dimensions (finite or infinite-dimensional). These bundles come with an important class of sections, which display properties reminiscent of classical nonlinear Fredholm theory and allow for implicit function theorems. Within this nonlinear analysis framework, a versatile transversality and perturbation theory is developed to also cover equivariant settings. The theory presented in this book was initiated by the authors between 2007-2010, motivated by nonlinear moduli problems in symplectic geometry. Such problems are usually described locally as nonlinear elliptic systems, and they have to be studied up to a notion of isomorphism. This introduces symmetries, since such a system can be isomorphic to itself in different ways. Bubbling-off phenomena are common and have to be completely understood to produce algebraic invariants. This requires a transversality theory for bubbling-off phenomena in the presence of symmetries. Very often, even in concrete applications, geometric perturbations are not general enough to achieve transversality, and abstract perturbations have to be considered. The theory is already being successfully applied to its intended applications in symplectic geometry, and should find applications to many other areas where partial differential equations, geometry and functional analysis meet. Written by its originators, Polyfold and Fredholm Theory is an authoritative and comprehensive treatise of polyfold theory. It will prove invaluable for researchers studying nonlinear elliptic problems arising in geometric contexts.
Author : Vladimir Müller
Publisher : Birkhäuser
Page : 390 pages
File Size : 53,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783034877886
This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. Many results appear here for the first time in a monograph.
Author : Celso Melchiades Doria
Publisher : Springer Nature
Page : 362 pages
File Size : 41,5 Mb
Release : 2021-07-19
Category : Mathematics
ISBN : 9783030778347
This book is divided into two parts, the first one to study the theory of differentiable functions between Banach spaces and the second to study the differential form formalism and to address the Stokes' Theorem and its applications. Related to the first part, there is an introduction to the content of Linear Bounded Operators in Banach Spaces with classic examples of compact and Fredholm operators, this aiming to define the derivative of Fréchet and to give examples in Variational Calculus and to extend the results to Fredholm maps. The Inverse Function Theorem is explained in full details to help the reader to understand the proof details and its motivations. The inverse function theorem and applications make up this first part. The text contains an elementary approach to Vector Fields and Flows, including the Frobenius Theorem. The Differential Forms are introduced and applied to obtain the Stokes Theorem and to define De Rham cohomology groups. As an application, the final chapter contains an introduction to the Harmonic Functions and a geometric approach to Maxwell's equations of electromagnetism.
Author : Caradus
Publisher : Routledge
Page : 160 pages
File Size : 55,9 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351462778
Since the appearance of Banach algebra theory, the interaction between the theories ofBanach algebras with involution and that of bounded linear operators on a Hilbert space hasbeen extensively developed. The connections of Banach algebras with the theory ofbounded linear operators on a Hilbert space have also evolved, and Calkin Algebras andAlgebras of Operators on Banach Spaces provides an introduction to this set of ideas.The book begins with a treatment of the classical Riesz-Schauder theory which takesadvantage of the most recent developments-some of this material appears here for the firsttime. Although the reader should be familiar with the basics of functional analysis, anintroductory chapter on Banach algebras has been included. Other topics dealt with includeFredholm operators, semi-Fredholm operators, Riesz operators. and Calkin algebras.This volume will be of direct interest to both graduate students and research mathematicians.
Author : H. Garth Dales
Publisher : Cambridge University Press
Page : 338 pages
File Size : 41,6 Mb
Release : 2003-11-13
Category : Mathematics
ISBN : 0521535840
Table of contents
Author : Vitaly Volpert
Publisher : Springer Science & Business Media
Page : 649 pages
File Size : 55,6 Mb
Release : 2011-03-03
Category : Mathematics
ISBN : 9783034605373
The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments . The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.
Author : Martin Krause
Publisher : Tectum Verlag DE
Page : 92 pages
File Size : 55,8 Mb
Release : 1996
Category : Banach algebras
ISBN : 3896089382
Author : Ronald G. Douglas
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 41,6 Mb
Release : 1998-07-27
Category : Mathematics
ISBN : 0387983775
A discussion of certain advanced topics in operator theory, providing the necessary background while assuming only standard senior-first year graduate courses in general topology, measure theory, and algebra. Each chapter ends with source notes which suggest additional reading along with comments on who proved what and when, followed by a large number of problems of varying difficulty. This new edition will appeal to a whole new generation of students seeking an introduction to this topic.
Author : Sandy Grabiner
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 51,8 Mb
Release : 1974
Category : Banach algebras
ISBN : 9780821818466
This paper studies derivations, endomorphisms, automorphisms, and various related questions about certain Banach algebras, B, which are continuously embedded in the space of complex formal power series in the indeterminate z.