About the Book
This text, Functional Analysis, based on the lecture notes of distinguished authors, is designed to cater to the needs of students who are yet to be exposed to the subject, as well as senior undergraduate- and graduate-level students at universities the world over. This text begins with a preliminary chapter that establishes uniform notations and covers background material in real analysis, linear algebra, and metric spaces. It is followed by chapters on Normed and Banach Spaces, Bounded Linear Operators and Bounded Linear Functional. This text also deals with the concept and specific geometry of Hilbert Spaces, Functional and Operators on Hilbert Spaces, and Introduction to Spectral Theory. The appendix provides an introduction to Schauder Bases. The first edition of this text was published in 1995. Since then, many mathematical developments have taken place, and the authors, too, have revised their lecture notes to provide further clarity for their students. As a result, the second edition, written in a more simple and lucid language and illustrated with familiar examples, should be an ideal textbook for easy comprehension of the subject. The clear explanations, numerous examples, problems, and illustrative figures also make the text invaluable for self-study and as a reference book. This edition is for sale in India, Bangladesh, Bhutan, Maldives, Nepal, Myanmar, Pakistan and Sri Lanka only. About the AuthorPawan Kumar Jain (b. 1942) - Fellow of the National Academy of Sciences (F.N.A.Sc); Emeritus Fellow (U.G.C.) and formerly, Professor and Head, Department of Mathematics, University of Delhi, having teaching and research experience of 43 years, has published 130 research papers and 12 expository articles in areas of Complex Analysis, Functional Analysis, Sobolev Spaces, Hardy-type Inequalities and Operators, Theory of Frames; supervised 24 Ph.Ds and 27 M.Phils; published six textbooks and edited twelve volumes. He has travelled widely in India and abroad for academic activities; besides his visits to USA, Canada, Germany, Kuwait, Sudan, Tanzania, Iran, Hong Kong, Jordan, China and Pakistan. He was nominated by the Indian National Science Academy to visit U.K. for three weeks during 2000-01 under the Exchange of Scientists Programme between INSA and Royal Society of London. He was awarded Visiting Professorship at Yarmouk University under the Joint Professorship Programme in Science and Sustainable Development of ISCU/TWAS/UNESCO/CSE/ Earth Council for a period of five years (1996-01). By now he has delivered several invited talks/colloquium lectures in India and abroad including the lectures at the University of Sussex, Imperial College of London and University of Oxford in UK; Auburn University, Tuskegee University and Clemson University in USA; McMaster University in Canada, Chinese University of Hong Kong. He was a member on the Curriculum Development Committee in Mathematics appointed by the UGC to frame syllabi at UG and PG levels. He has worked on several academic bodies/committees of UGC, DST, CSIR, MHRD, N.C.E.R.T. etc. Om P. Ahuja, recipient of 30 international recognitions and funded grants, including the National Science Foundation Grant (USA, 2005) and two times nominee of the US Professors of the Year Award (2005, 2006), currently serves as an Associate Professor of Mathematics at Kent State University in Ohio, USA. He has taught for more than 39 years at many international institutions including the University of California (Davis), Nanyang Technological University in Singapore, University of Khartoum in Sudan, and the University of Addis Ababa in Ethiopia and D.A.V. College, Abohar. He served as Head of the Mathematics Department and Associate Dean of the Faculty of Science at the University of Papua New Guinea. Prior to his international work, Dr. Ahuja was a recipient of the esteemed one year Teaching Fellowship at the University of Bombay and Tata Institute of Fundamental Research in Bombay. He has lectured or presented papers at over 80 national and international conferences and universities. He served as the Chief Organizer or Chairman of international conferences including the first South Pacific Conference on Mathematics and Mathematics Education in Papua New Guinea (1992) and the Conference on Challenges of Calculus Educations in Singapore (1998). Dr. Ahujas research interests include complex analysis, functional analysis, and mathematics education. He has contributed over 100 papers to mathematics and mathematics education journals and has served as a reviewer for the American Mathematical Society for the past 25 years.Table of ContentsPreliminariesNormed and Banach SpacesBounded Linear OperatorsBounded Linear FunctionalsThe Concept and Specific Geometry of Hilbert SpacesFunctionals and Operators on Hilbert SpacesIntroduction to Spectral TheoryAppendix : Schauder BasesBibliographyIndex