The Analyst’s Gambit by Shalit, Orr Moshe;

Short description:

The Analyst’s Gambit: A Second Course in Functional Analysis is a textbook written to serve a graduate course in Functional Analysis. It provides a sequel to the author’s other volume, A First Course in Functional Analysis, but it is not necessary to have read one in order to make use of the other.

Long description:

The Analyst’s Gambit: A Second Course in Functional Analysis is a textbook written to serve a graduate course in Functional Analysis. It provides a sequel to the author’s previous volume, A First Course in Functional Analysis, but it is not necessary to have read one in order to make use of the other. As a graduate text, the reader is assumed to have taken undergraduate courses in set theory, calculus, metric spaces and topology, complex analysis, measure theory (or, alternatively, have enough mathematical maturity to carry on without having seen every particular fact that is used).

A particular strength of the book is that it includes numerous applications. Besides being engaging and interesting in their own right, these applications also illustrate how functional analysis is used in other parts of mathematics. The applications to problems from varied fields (PDEs, Fourier series, group theory, neural networks, topology, etc.) constitute an enticing external motivation for studying functional analysis. There are also applications of the material to functional analytic problems (Lomonosov’s invariant subspace theorem, the spectral theorem, Stone’s theorem), showcasing the power of the results as well as the elegance and unity of the theory.

• Can be used as the primary textbook for a graduate course in functional analysis

• Rich variety of exercises

• Emphasis on substantial and modern applications

Orr Moshe Shalit is a professor of mathematics at the Technion Israel Institute of Technology, where he teaches and conducts research in operator theory, operator algebras, functional analysis and function theory. His first book, A First Course in Functional Analysis, was published by Chapman & Hall / CRC in 2017.

Table of Contents:

Preface 1. Basic notions and first examples of Banach spaces 2. The Hahn–Banach theorems and duality 3. The dual spaces of Lp and C0(X) 4. The open mapping, uniform boundedness and closed graph theorems 5. Further aspects of duality: weak convergence and the adjoint 6. Locally convex spaces and weak topologies 7. The Krein–Milman theorem and applications 8. Banach algebras 9. Commutative Banach algebras 10. C*-algebras 11. The spectral theorem and von Neumann algebras 12. Representations of C*-algebras 13. Unbounded operators Bibliography Index