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040			_cIISER-BPR
041			_aENG
082			_a515.7 _bKES _223rd
100			_aKesavan, S.
222			_aMathematics
245		0	_aFunctional analysis
250			_a2nd ed.
260			_aNew Delhi: _bHindustan Book Agency, _cc2022.
300			_axiv, 287p. : _bpbk. ; _c24cm.
440			_aTexts and readings in mathematics _vVol. 52
520			_aThis book is suited for a first course on Functional Analysis at the masters level. Efforts have been made to illustrate the use of various results via examples taken from differential equations and the calculus of variations, either through brief sections or through exercises. So, this book will be particularly useful for students who aspire to a research career in the applications of mathematics. Special emphasis has been given to the treatment of weak topologies and their applications to notions like reflexivity, separability and uniform convexity. The chapter on Lebesgue spaces includes a section devoted to the simplest examples of Sobolev spaces. The chapter on compact operators includes the spectral theory of compact self-adjoint operators on a Hilbert space. Each chapter concludes with a large selection of exercises of varying degrees of difficulty. They often provide examples or counter-examples to illustrate the optimality of the hypotheses of various theorems proved in the text, or develop simple versions of theories not developed therein. In this (second) edition, the book has been completely overhauled, without altering its original structure. Proofs of many results have been rewritten for greater clarity of exposition. Many examples have been added to make the text more user-friendly. Several new exercises have been added. Contents :- 1Preliminaries 2 Normed Linear Spaces 3 Hahn-Banach Theorems 4 Baire's Theorem and Applications 5 Weak and Weak* Topologies 6 Lp Spaces 7 Hilbert Spaces 8 Compact Operators Bibliography/Index
650			_aMathematics
650			_aAnalysis
650			_aFunctional Analysis
942			_cBK _2ddc
942			_2ddc
947			_a850
948			_a0.22
999			_c4084 _d4084