An Invitation to Functional Analysis

Ben de Pagter, Arnoud van Rooij

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This book aims to make the reader acquainted with the fundamental ideas of Functional Analysis avoiding unnecessary abstractions. Indeed, much more than is commonly realized can be done in this vein. As a case in point, all what is used of topology is some elementary theory of metric spaces (developed in the book itself). Admittedly, the approach of the authors limits the generality of the results. This limitation, however, turns out to be of little importance for practical applications. Globally speaking, this book covers normed vector spaces, Banach spaces and Hilbert spaces (without going into topological vector spaces or Banach algebras). Integration theory is treated in an appendix. There is an ample collection of exercises.

Auteur(s)
Inhoudsopgave

Ben de Pagter was born in 1953 in Den Haag. He obtained his Ph.D. degree in 1981 at the Leiden University under the supervision of A.C. Zaanen. He stayed for two years at the California Institute of Technology and received several research fellowships. In 1989 he was appointed as an assistant professor at the Delft University of Technology, where he was given a full professorship in Analysis in 2005. His fields of research are the theory of Positive Operators and Non-commutative Integration Theory.

Arnoud van Rooij was born in 1936 in Eindhoven. He obtained his Ph.D. degree at the Utrecht University with H. Freudenthal as his advisor. For two years he stayed at the University of Pennsylvania. In 1965 he was appointed as a ’lector’ at the (now) Radboud University at Nijmegen, where he was given a full professorship in 1971. His field of research is Analysis, more specifically non-Archimedean Analysis and the Theory of Riesz Spaces. In 2001 he retired.

I. Metric Spaces
II. Normed Vector Spaces
III. Linear Operators
IV. Banach Spaces
V. Hilbert Spaces

Appendix A. Conventions and Notations
Appendix B. Linear Algebra
Appendix C. Integration Theory