Introduction to Modern Analysis

Description

Aimed at advanced undergraduate and graduate students this textbook provides an introduction to
the vast and crucial area of modern analysis. This new edition begins by covering the theoretical bases, gradually moving on to more advanced subjects and practical applications, supplementing the material with many exercises.

• Covers a wide range of topics, starting from undergraduate modern analysis and progressing gradually to advanced graduate-level topics
• Includes numerous exercises, which cover some important results beyond what is provided in the main text

New to this edition

• Devotes several new chapters to operator algebras, a central area in functional analysis
• Includes several other advanced topics such as Von Neumann algebras, tensor products of C*-algebras, and group C*-algebras
• Contains many new exercises

About the Author(s)

Shmuel Kantorovitz, Professor Emeritus of Mathematics, Bar-Ilan University, and Ami Viselter, Senior Lecturer, University of Haifa

Shmuel Kantorovitz received his Ph.D. from the University of Minnesota in 1962. After postdocs at Princeton University and the Institute for Advanced Study in Princeton, he took on an Assistant Professorship at Yale University, and became an Associate and then Full Professor at the University of Illinois in Chicago. He then returned to Israel to become a Full Professor at Bar-Ilan University, where he is now Professor Emeritus.

Ami Viselter received his Ph.D. from Bar-Ilan University in 2009. After postdocs in the Technion - Israel Institute of Technology and at the University of Alberta, he became a faculty member at the University of Haifa, where he is currently a tenured Senior Lecturer.

Table of Contents

1:Measures
2:Construction of measures
3:Measure and topology
4:Continuous linear functionals
5:Duality
6:Bounded operators
7:Banach algebras
8:Hilbert spaces
9:Integral representation
10:Unbounded operators
11:C*-algebras
12:Von Neumann algebras
13:Constructions of C*-algebras
Application I
Probability
Application II
Distributions