Linear Functional Analysis for Scientists and Engineers

1. Front Matter

   Pages i-xiv

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2. Prerequisites

   • Balmohan V. Limaye

   Pages 1-32

3. Basic Framework

   • Balmohan V. Limaye

   Pages 33-74

4. Bounded Linear Maps

   • Balmohan V. Limaye

   Pages 75-118

5. Dual Spaces, Transposes and Adjoints

   • Balmohan V. Limaye

   Pages 119-158

6. Spectral Theory

   • Balmohan V. Limaye

   Pages 159-202

7. Correction to: Linear Functional Analysis for Scientists and Engineers

   • Balmohan V. Limaye

   Pages C1-C1

8. Back Matter

   Pages 203-255

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This book provides a concise and meticulous introduction to functional analysis. Since the topic draws heavily on the interplay between the algebraic structure of a linear space and the distance structure of a metric space, functional analysis is increasingly gaining the attention of not only mathematicians but also scientists and engineers. The purpose of the text is to present the basic aspects of functional analysis to this varied audience, keeping in mind the considerations of applicability. A novelty of this book is the inclusion of a result by Zabreiko, which states that every countably subadditive seminorm on a Banach space is continuous. Several major theorems in functional analysis are easy consequences of this result.


The entire book can be used as a textbook for an introductory course in functional analysis without having to make any specific selection from the topics presented here. Basic notions in the setting of a metric space are defined in terms of sequences. These include total boundedness, compactness, continuity and uniform continuity. Offering concise and to-the-point treatment of each topic in the framework of a normed space and of an inner product space, the book represents a valuable resource for advanced undergraduate students in mathematics, and will also appeal to graduate students and faculty in the natural sciences and engineering. The book is accessible to anyone who is familiar with linear algebra and real analysis.

• Adjoint of a Bounded Linear Map
• Approximate Eigenspectrum
• Banach Space
• Bounded Inverse Theorem
• Bounded Linear Map
• Closed Graph Theorem
• Compact Linear Map
• Dual Space
• Eigenspectrum
• Hahn-Banach Theorems
• Hilbert Space
• Normal Operator
• Open Mapping Theorem
• Self-adjoint Operator
• Spectral Theory
• Spectrum of a Bounded Operator
• Transpose of a Bounded Linear Map
• Uniform Boundedness Principle
• Unitary Operator
• Zabreiko Theorem

“The title of this book indicates that it is mainly devoted to linear maps on linear spaces. … All chapters are accompanied by useful exercises of varying levels of difficulty, which help the readers to develop their knowledge on the topics. The solutions of the exercises are given at the end of the book. … This textbook is essentially addressed to people working in engineering and sciences branches.” (Mohammad Sal Moslehian, zbMATH 1352.46001, 2017)

“A textbook designed for an initial but sophisticated study of a classical compulsory course in the modern mathematical education … . a significant part of the book is devoted to examples illustrating the concepts introduced and the results proved earlier. Each chapter (except the first) ends with 40 well-selected and interesting exercises which essentially complement the main text. At the end of the book, solutions to all these exercises are given. In conclusion, the book is interesting and useful. The simplicity and clarity in the presentation of basic ideas and results, the absence of cumbersome arguments, and a good set of exercises make the book easily readable and valuable to all mathematicians: students, teachers and researchers.” (Prof. Petr P. Zabreiko, Belarussian State University at Minsk, Belarus)

• Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai Mumbai, India

  Balmohan V. Limaye

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 in refereed 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).

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