Author: David E. Edmunds
Publisher: Springer Science & Business Media
ISBN: 3034806426
Category : Mathematics
Languages : en
Pages : 164
Book Description
The book deals with the representation in series form of compact linear operators acting between Banach spaces, and provides an analogue of the classical Hilbert space results of this nature that have their roots in the work of D. Hilbert, F. Riesz and E. Schmidt. The representation involves a recursively obtained sequence of points on the unit sphere of the initial space and a corresponding sequence of positive numbers that correspond to the eigenvectors and eigenvalues of the map in the Hilbert space case. The lack of orthogonality is partially compensated by the systematic use of polar sets. There are applications to the p-Laplacian and similar nonlinear partial differential equations. Preliminary material is presented in the first chapter, the main results being established in Chapter 2. The final chapter is devoted to the problems encountered when trying to represent non-compact maps.
Representations of Linear Operators Between Banach Spaces
Author: David E. Edmunds
Publisher: Springer Science & Business Media
ISBN: 3034806426
Category : Mathematics
Languages : en
Pages : 164
Book Description
The book deals with the representation in series form of compact linear operators acting between Banach spaces, and provides an analogue of the classical Hilbert space results of this nature that have their roots in the work of D. Hilbert, F. Riesz and E. Schmidt. The representation involves a recursively obtained sequence of points on the unit sphere of the initial space and a corresponding sequence of positive numbers that correspond to the eigenvectors and eigenvalues of the map in the Hilbert space case. The lack of orthogonality is partially compensated by the systematic use of polar sets. There are applications to the p-Laplacian and similar nonlinear partial differential equations. Preliminary material is presented in the first chapter, the main results being established in Chapter 2. The final chapter is devoted to the problems encountered when trying to represent non-compact maps.
Publisher: Springer Science & Business Media
ISBN: 3034806426
Category : Mathematics
Languages : en
Pages : 164
Book Description
The book deals with the representation in series form of compact linear operators acting between Banach spaces, and provides an analogue of the classical Hilbert space results of this nature that have their roots in the work of D. Hilbert, F. Riesz and E. Schmidt. The representation involves a recursively obtained sequence of points on the unit sphere of the initial space and a corresponding sequence of positive numbers that correspond to the eigenvectors and eigenvalues of the map in the Hilbert space case. The lack of orthogonality is partially compensated by the systematic use of polar sets. There are applications to the p-Laplacian and similar nonlinear partial differential equations. Preliminary material is presented in the first chapter, the main results being established in Chapter 2. The final chapter is devoted to the problems encountered when trying to represent non-compact maps.
History of Banach Spaces and Linear Operators
Author: Albrecht Pietsch
Publisher: Springer Science & Business Media
ISBN: 0817645969
Category : Mathematics
Languages : en
Pages : 877
Book Description
Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Publisher: Springer Science & Business Media
ISBN: 0817645969
Category : Mathematics
Languages : en
Pages : 877
Book Description
Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Spear Operators Between Banach Spaces
Author: Vladimir Kadets
Publisher: Springer
ISBN: 3319713337
Category : Mathematics
Languages : en
Pages : 176
Book Description
This monograph is devoted to the study of spear operators, that is, bounded linear operators G between Banach spaces X and Y satisfying that for every other bounded linear operator T:X → Y there exists a modulus-one scalar ω such that ǁ G+ωTǁ = 1 + ǁTǁ. This concept extends the properties of the identity operator in those Banach spaces having numerical index one. Many examples among classical spaces are provided, being one of them the Fourier transform on L1. The relationships with the Radon-Nikodým property, with Asplund spaces and with the duality, and some isometric and isomorphic consequences are provided. Finally, Lipschitz operators satisfying the Lipschitz version of the equation above are studied. The book could be of interest to young researchers and specialists in functional analysis, in particular to those interested in Banach spaces and their geometry. It is essentially self-contained and only basic knowledge of functional analysis is needed.
Publisher: Springer
ISBN: 3319713337
Category : Mathematics
Languages : en
Pages : 176
Book Description
This monograph is devoted to the study of spear operators, that is, bounded linear operators G between Banach spaces X and Y satisfying that for every other bounded linear operator T:X → Y there exists a modulus-one scalar ω such that ǁ G+ωTǁ = 1 + ǁTǁ. This concept extends the properties of the identity operator in those Banach spaces having numerical index one. Many examples among classical spaces are provided, being one of them the Fourier transform on L1. The relationships with the Radon-Nikodým property, with Asplund spaces and with the duality, and some isometric and isomorphic consequences are provided. Finally, Lipschitz operators satisfying the Lipschitz version of the equation above are studied. The book could be of interest to young researchers and specialists in functional analysis, in particular to those interested in Banach spaces and their geometry. It is essentially self-contained and only basic knowledge of functional analysis is needed.
Introduction to Linear Operator Theory
Author: Vasile I. Istratescu
Publisher: CRC Press
ISBN: 1000146324
Category : Mathematics
Languages : en
Pages : 605
Book Description
This book is an introduction to the subject and is devoted to standard material on linear functional analysis, and presents some ergodic theorems for classes of operators containing the quasi-compact operators. It discusses various classes of operators connected with the numerical range.
Publisher: CRC Press
ISBN: 1000146324
Category : Mathematics
Languages : en
Pages : 605
Book Description
This book is an introduction to the subject and is devoted to standard material on linear functional analysis, and presents some ergodic theorems for classes of operators containing the quasi-compact operators. It discusses various classes of operators connected with the numerical range.
Representation Theorems on Banach Function Spaces
Author: Neil E. Gretsky
Publisher: American Mathematical Soc.
ISBN: 082181284X
Category : Banach spaces
Languages : en
Pages : 60
Book Description
Publisher: American Mathematical Soc.
ISBN: 082181284X
Category : Banach spaces
Languages : en
Pages : 60
Book Description
Construction of Representations of Commutation Relations by Linear Operators in Banach Spaces
Author: Domingos Djinja
Publisher:
ISBN: 9789174855944
Category :
Languages : en
Pages : 0
Book Description
Publisher:
ISBN: 9789174855944
Category :
Languages : en
Pages : 0
Book Description
Investigations in Linear Operators and Function Theory
Author: Nikolaĭ Kapitonovich Nikolʹskiĭ
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 152
Book Description
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 152
Book Description
Linear Representations of the Lorentz Group
Author: M. A. Naimark
Publisher: Elsevier
ISBN: 1483184986
Category : Mathematics
Languages : en
Pages : 465
Book Description
Linear Representations of the Lorentz Group is a systematic exposition of the theory of linear representations of the proper Lorentz group and the complete Lorentz group. This book consists of four chapters. The first two chapters deal with the basic material on the three-dimensional rotation group, on the complete Lorentz group and the proper Lorentz group, as well as the theory of representations of the three-dimensional rotation group. These chapters also provide the necessary basic information from the general theory of group representations. The third chapter is devoted to the representations of the proper Lorentz group and the complete Lorentz group, while the fourth chapter examines the theory of invariant equations. This book will prove useful to mathematicians and students.
Publisher: Elsevier
ISBN: 1483184986
Category : Mathematics
Languages : en
Pages : 465
Book Description
Linear Representations of the Lorentz Group is a systematic exposition of the theory of linear representations of the proper Lorentz group and the complete Lorentz group. This book consists of four chapters. The first two chapters deal with the basic material on the three-dimensional rotation group, on the complete Lorentz group and the proper Lorentz group, as well as the theory of representations of the three-dimensional rotation group. These chapters also provide the necessary basic information from the general theory of group representations. The third chapter is devoted to the representations of the proper Lorentz group and the complete Lorentz group, while the fourth chapter examines the theory of invariant equations. This book will prove useful to mathematicians and students.
Spectral Representations of Linear Operator
Author: Kurt Otto Friedrichs
Publisher:
ISBN:
Category : Algebra, Universal
Languages : en
Pages : 394
Book Description
Publisher:
ISBN:
Category : Algebra, Universal
Languages : en
Pages : 394
Book Description
Spectral Theory of Banach Space Operators
Author: S. Kantorovitz
Publisher: Springer
ISBN: 3540386661
Category : Mathematics
Languages : en
Pages : 184
Book Description
Publisher: Springer
ISBN: 3540386661
Category : Mathematics
Languages : en
Pages : 184
Book Description