Balmohan V. Limaye is adjunct professor at the Department of Mathematics, Indian Institute of Technology (IIT) Bombay, where he has been working for more than 40 years. Earlier, he worked at the University of California at Irvine (USA), for one year and the Tata Institute of Fundamental Research (TIFR), Mumbai, for six years. Professor Limaye has made research visits to the University of Grenoble (France); the Australian National University at Canberra; the University of Saint-Étienne (France); the University of Tübingen (Germany); Oberwolfach Research Institute for Mathematics (Germany); the University of California at Irvine (USA); the University of Porto (Portugal), and the Technical University of Berlin (Germany).

Professor Limaye earned his PhD in mathematics from the University of Rochester, New York, in 1969. His research interests include algebraic analysis, numerical functional analysis and linear algebra. He has published more than 50 articles inrefereed journals. In 1995, he was invited by the Indian Mathematical Society (IMS) to deliver the Sixth Srinivasa Ramanujan Memorial Award Lecture. In 1999 and in 2014, he received the "Award for Excellence in Teaching" from the IIT Bombay. An International Conference on "Topics in Functional Analysis and Numerical Analysis" was held in his honour in 2005, and its proceedings were published in a special issue of The Journal of Analysis in 2006. He is an emeritus member of the American Mathematical Society and a life member of the Indian Mathematical Society.

He is author/coauthor of several books: (i) Textbook of Mathematical Analysis (Tata McGraw-Hill, 1980), (ii) Functional Analysis (Wiley Eastern, 1981; New Age International, 1996), (iii) Spectral Perturbation and Approximation with Numerical Experiments (Australian National University, 1987), (iv) Real Function Algebras (Marcel Dekker, 1992), (v) Spectral Computations for Bounded Operators (CRC Press, 2001), (vi) A Course in Calculus and Real Analysis (Springer, 2006), and (vii) A Course in Multivariable Calculus and Analysis (Springer, 2010).

Provides a concise introduction to linear functional analysis

Presents results in the basic framework of a normed space and of an inner product space

Includes a result by Zabreiko, which is used to deduce several major theorems in functional analysis

Contains 160 exercises of various difficulty levels, and their solutions provided at the end of the book

Will benefit senior undergraduate students in mathematics and graduate students in the natural sciences and engineering

Includes supplementary material: [...]

Chapter 1. Preliminaries.- Chapter 2. Basic Framework.- Chapter 3. Bounded Linear Maps.- Chapter 4. Dual Spaces, Transposes and Adjoints.- Chapter 5. Spectral Theory.