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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.
List 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
About the author
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.
Summary
This textbook provides an introduction to modern analysis aimed at advanced undergraduate and graduate-level students of mathematics. Professional academics will also find this to be a useful reference work. It covers measure theory, basic functional analysis, single operator theory, spectral theory of bounded and unbounded operators, semigroups of operators, and Banach algebras. Further, this new edition of the textbook also delves deeper into C*-algebras and their standard constructions, von Neumann algebras, probability and mathematical statistics, and partial differential equations.
Most chapters contain relatively advanced topics alongside simpler ones, starting from the very basics of modern analysis and slowly advancing to more involved topics. The text is supplemented by many exercises, to allow readers to test their understanding and practical analysis skills.
Additional text
Most chapters contain relatively advanced topics alongside simpler ones, starting from the very basics of modern analysis and slowly advancing to more involved topics. The text is supplemented by many exercises, to allow readers to test their understanding and practical analysis skills.
