Functional AnalysisFunctional Analysis, written in a clear and entertaining style for senior and postgraduate students discusses Hilbert spaces, Banach algebras, Operator theory and Topological vector spaces. The book covers many standard results including the Hahn-Banach, open mapping and closed graph theorems; the Banach-Steinhaus and the Banach-Alaoglu theorems; Riesz-Fischer and Riesz representation theorems; Gelfand-Mazur and Gelfand-Neumark theorems; Bipolar theorem; and the Kolmogoroff criterion for normability. The book is designed for senior undergraduate and postgraduate students of mathematics and mathematical physics. |
Contents
Preface to the Second Edition | 1 |
Normed Spaces | 23 |
Hilbert Spaces | 88 |
Copyright | |
6 other sections not shown
Common terms and phrases
A₁ absolutely convex B₁ Banach algebra Banach space bounded linear operator bounded linear transformation bounded sequence bounded set Cauchy sequence closed linear subspace closed unit ball compact operator complete continuous linear functional convergent subsequence countable defined Definition Let denote eigen value exists extreme point finite Functional Analysis Hence Hilbert space implies Inequality inner-product space invariant isometry Lemma Let f linear subspace locally convex space metric space non-zero normal operator normed linear space normed space operator on H orthonormal basis P₁ perpendicular projection positive integer Problem Proof Let Proof Step Prove real number scalar self-adjoint operator Solution Let space and let space H Step 2 Suppose subset surjective T₁ T₂ Theorem topological vector space totally bounded unitary whence x₁ zero