Edited by
W.B. Johnson, Texas A&M University, TX, USA
J. Lindenstrauss, The Hebrew University of Jerusalem, Israel
Handbook of the Geometry of Banach Spaces, Volume 1
Description
The Handbook presents an overview of most aspects of modern Banach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations.
The Handbook begins with a chapter on basic concepts in Banach space theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers.
As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.
Audience
University libraries and libraries connected to departments of Mathematics, Statistics, Theoretical Computer Science and individual mathematicians.
Contents
1. Basic concepts in the geometry of Banach spaces (W.B. Johnson, J. Lindenstrauss)
2. Positive operators (Y.A. Abramovitch, C.D. Aliprantis)
3. Lp spaces (D. Alspach, E. Odell)
4. Convex geometry and functional analysis (K. Ball)
5. A p-sets in analysis: Results, problems and related aspects (J. Bourgain)
6. Martingales and singular integrals in Banach spaces (D.L. Burkholder)
7. Approximation properties (P.G. Casazza)
8. Local operator theory, random matrices and Banach spaces (K.R. Davidson, S.J. Szarek)
9. Applications to mathematical finance (F. Delbaen)
10. Perturbed minimization principles and applications (R. Deville, N. Ghoussoub)
11. Operator ideals (J. Diestel, H. Jarchow, A. Pietsch)
12. Special Banach lattices and their applications(S.J. Dilworth)
13. Some aspects of the invariant subspace problem (P. Enflo,V. Lomonosov)
14. Special bases in function spaces (T. Figel, P. Wojtaszczyk)
15. Infinite dimensional convexity (V. Fonf, J. Lindenstrauss, R.R. Phelps)
16. Uniform algebras as Banach spaces (T.W. Gamelin, S.V. Kisliakov)
17. Euclidean structure in finite dimensional normed spaces (A.A. Giannopoulos, V.D. Milman)
18. Renormings of Banach spaces (G. Godefroy)
19. Finite dimensional subspaces of Lp (W.B. Johnson, G. Schechtman)
20. Banach spaces and classical harmonic analysis (S.V. Kisliakov)
21. Aspects of the isometric theory of Banach spaces (A. Koldobsky, H. Konig)
22. Eigenvalues of operators and applications (H. Konig)
Year 2001
Hardbound
ISBN: 0-444-82842-7
1016 pages
Edited by
K.D. Bierstedt, Universitat-Gesamthochschule Paderborn, Paderborn, Germany
J. Bonet, Unversidad de Valencia, Departamento de Matematica Aplicada, Valencia, Spain
M. Maestre, University of Valencia, Departamento de Analisis Matematico, Valencia, Spain
J. Schmets, Universite de Liege, Institut de Mathematique, Liege, Belgium
Recent Progress in Functional Analysis
North-Holland Mathematics Studies, 189
Description
This Proceedings Volume contains 32 articles on various interesting areas of present-day functional analysis and its applications: Banach spaces and their geometry, operator ideals, Banach and operator algebras, operator and spectral theory, Frechet spaces and algebras, function and sequence spaces. The authors have taken much care with their articles and many papers present important results and methods in active fields of research. Several survey type articles (at the beginning and the end of the book) will be very useful for mathematicians who want to learn "what is going on" in some particular field of research.
Contents
List of sponsors and committees. Schedule. List of the special sessions. Schedules of the special sessions. Schedule of the poster sessions. List of participants. List of contributors.
The mathematical works of Manuel Valdivia, II (J. Schmets).
Frechet differentiability of Lipschitz functions (a survey) (J. Lindenstrauss, D. Preiss).
Summing inclusion maps between symmetric sequence spaces, a survey (A. Defant, M. Mastylo, C. Michels).
Applications of Banach space theory to sectorial operators (N. Kalton).
Derivations from Banach algebras (H.G. Dales).
Homomorphisms of uniform algebras (T.W. Gamelin).
Generic Dynamics and monotone complete C*-algebras (J.D. Maitland Wright).
Linear topological properties of the space of analytic functions on the real line (P. Domanski, D. Vogt).
Contribution to the isomorphic classification of Sobolev spaces Lp(k)( )
(1 p< )
(A. Pelczynski, D. Vogt).
Decomposability and the cyclic behavior of parabolic composition operators (J.H. Shapiro).
Algebras of subnormal operators on the unit polydisc (J. Eschmeier).
An example concerning the local radial Phragman-Lindelof condition (R.W. Braun, R. Meise, B.A. Taylor).
Continuity of monotone functions with values in Banach lattices (L. Drewnowski).
Remarks on Gowers' dichotomy (A.M. Pelczar).
Norm attaining operators and James' theorem (M.D. Acosta, J. Becerra Guerrero, M. Ruiz Galan).
The extension theorem for norms on symmetric tensor products of normed spaces (K. Floret).
Remarks on p-summing multipliers (O. Blasco).
Bergman projection on simply connected domains (J. Taskinen).
On isomorphically equivalent extensions of quasi-Banach spaces (J.M.F. Castillo, Y. Moreno).
Integrated trigonometric sine functions (P.J. Miana).
Applications of a result of Aron, Herves, and Valdivia to the homology of Banach algebras (F. Cabello Sanchez, R. Garcia).
On the ideal structure of some algebras with an Arens product (M. Filali).
Stochastic continuity algebras (B.M. Schreiber).
Hilbert space methods in the theory of Lie triple systems (A.J. Calderon Martin, C. Martin Gonzalez).
Truncated Hamburger moment problems with constraints (V.M. Adamyan, I.M. Tkachenko).
Fourier-Bessel transformation of measures and singular differential equations (A.B. Muravnik).
A trace theorem for normal boundary conditions (M. Poppenberg).
Operators into Hardy spaces and analytic Pettis integrable functions (F.J. Freniche, J.C. Garcia-Vazquez, L. Rodriguez-Piazza).
The norm problem for elementary operators (M. Mathieu).
Problems on Boolean algebras of projections in locally convex spaces (W.J. Ricker).
Non associative C*-algebras revisited (K. El Amin, A. Morales Campoy, A. Rodriguez Palacios).
Grothendieck's inequalities revisited (A.M. Peralta, A. Rodriguez Palacios).
Year 2001
Hardbound
ISBN: 0-444-50219-X
468 pages
Geoffrey Grimmett, Statistical Laboratory, University of Cambridge,
and David Stirzaker, Mathematical Institute, University of Oxford
One Thousand Exercises in Probability
Second Edition
Description
This is an updated and greatly expanded version of an already well-established and popular exercise manual. It provides a wide-ranging selection of illuminating, informative and entertaining problems, together with their solution.
Topics include modelling and many applications of probability theory, as well as theoretical aspects. There are questions at all ability levels, the majority being of elementary or intermediate standard.
Well suited as a stand alone problems and solutions manual, it also is the companion volume for the text: Probability and Random Processes 3/e.
Readership: Introductory, intermediate and advanced courses in probability and random (stochastic) processes at undergraduate and postgraduate level
Contents/contributors
1 Events and their probabilities
2 Random variables and their distribution
3 Discrete randon variables
4 Continuous random variables
5 Generating functions and their applications
6 Markov chains
7 Convergence of random variables
8 Random processes
9 Stationary processes
10 Renewals
11 Queues
12 Martingales
13 Diffusion processes
Table of distributions
Bibliography
Index
Paperback, 0-19-857221-2
Publication date: 24 May 2001
Yudi Pawitan, Department of Statistics, National University of Ireland, Cork
In All Likelihood
Statistical Modelling and Inference Using Likelihood
528 pages, 234mm x 156mm
Hardback, 0-19-850765-8
Publication date: 21 June 2001
Description
This book introduces likelihood as an unifying concept in statistical modelling and inference. The complete range of concepts and applications are covered, from very simple to very complex studies. The approach is largely informal, relying on realistic examples, and presents the main results using heuristic rather than formal mathematical arguments.
Readership: Advanced undergraduate students in statistics and mathematics. Beginning graduate students in statistics and mathematics. Traditionally-trained statisticians wanting to learn modern likelihood-based statistical methods.
Contents/contributors
1 Introduction
2 Elements of likelihood inference
3 More properties of the likelihood
4 Basic models and simple applications
5 Frequentist properties
6 Modelling relationships: regression models
7 Evidence and the likelihood principle
8 Score function and Fisher information
9 Large Sample Results
10 Dealing with nuisance parameters
11 Complex data structure
12 EM Algorithm
13 Robustness of likelihood specification
14 Estimating equation and quasi-likelihood
15 Empirical likelihood
16 Likelihood of random parameters
17 Random and mixed effects models
18 Nonparametric smoothing