Representations of Linear Operators Between Banach Spaces
Representations of Linear Operators Between Banach Spaces

Author: David E. Edmunds

Publisher: Springer Science & Business Media

Published: 2013-09-04

Total Pages: 164

ISBN-13: 3034806426

DOWNLOAD EBOOK

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
History of Banach Spaces and Linear Operators

Author: Albrecht Pietsch

Publisher: Springer Science & Business Media

Published: 2007-12-31

Total Pages: 877

ISBN-13: 0817645969

DOWNLOAD EBOOK

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
Spear Operators Between Banach Spaces

Author: Vladimir Kadets

Publisher: Springer

Published: 2018-04-16

Total Pages: 176

ISBN-13: 3319713337

DOWNLOAD EBOOK

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
Introduction to Linear Operator Theory

Author: Vasile I. Istratescu

Publisher: CRC Press

Published: 2020-08-14

Total Pages: 605

ISBN-13: 1000146324

DOWNLOAD EBOOK

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.

Linear Representations of the Lorentz Group
Linear Representations of the Lorentz Group

Author: M. A. Naimark

Publisher: Elsevier

Published: 2014-07-15

Total Pages: 465

ISBN-13: 1483184986

DOWNLOAD EBOOK

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.

Problems And Solutions In Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions And Quantum Mechanics
Problems And Solutions In Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions And Quantum Mechanics

Author: Willi-hans Steeb

Publisher: World Scientific

Published: 2022-08-23

Total Pages: 454

ISBN-13: 9811245746

DOWNLOAD EBOOK

This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions.The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included.

Denseness, Bases and Frames in Banach Spaces and Applications
Denseness, Bases and Frames in Banach Spaces and Applications

Author: Aref Jeribi

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-03-19

Total Pages: 513

ISBN-13: 3110492407

DOWNLOAD EBOOK

This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. Contents Introduction Linear operators Basic notations and results Bases Semi-groups Discrete operator and denseness of the generalized eigenvectors Frames in Hilbert spaces Summability of series ν-convergence operators Γ-hypercyclic set of linear operators Analytic operators in Béla Szökefalvi-Nagy’s sense Bases of the perturbed operator T(ε) Frame of the perturbed operator T(ε) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory