Representations of linear operators between Banach spaces
 Author/Creator
 Edmunds, D. E. (David Eric)
 Language
 English.
 Imprint
 Basel : Birkhäuser : Springer, c2013.
 Physical description
 x, 152 p. ; 25 cm.
 Series
 Operator theory, advances and applications ; v. 238.
Access
Available online

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Unknown
QA329.2 .E324 2013

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QA329.2 .E324 2013
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Contributors
 Contributor
 Evans, W. D.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 141146) and index.
 Contents

 Basic notation
 Preliminaries
 The geometry of Banach spaces
 Bases
 The ptrigonometric functions
 Entropy numbers and snumbers
 Fundamentals
 Gelfand numbers and widths
 Notes
 Representation of compact linear operators
 Compact operators in Hilbert spaces
 Compact operators in Banach spaces
 Preliminaries
 The linear projections Sk
 The nonlinear projections Pk : X : Xk
 The main convergence theorems
 A basis for X
 A Schmidttype expansion for T
 Applications
 The pLaplacian
 A weighted problem for the pLaplacian
 A pLaplacian problem in Rn
 The pbiharmonic operator
 SturmLiouville theory for the pLaplacian
 LusternikSchnirelmann critical levels
 Comparison of eigenvalues
 A hardytype operator
 Further consequences of the boundedness of (Sn)nEN
 Notes
 Representation of bounded linear operators
 An integral representation of points of X
 An integral representation for T
 Compact operators revisited
 Notes
 Bibliography
 Author Index
 Subject Index
 Notation Index.
 Publisher's Summary
 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 pLaplacian 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 noncompact maps.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 David E. Edmunds, W. Desmond Evans.
 Series
 Operator theory, advances and applications, 02550156 ; Volume 238
 Available in another form
 9783034806428 (online)
 (GyWOH)har130440488
 ISBN
 9783034806411
 3034806418