Functional Analysis: Lectures Given at New York University [Courant Institute] in 1960-611961 - Functional analysis - 133 pages |
Common terms and phrases
A₁ apply Baire Category Theorem Banach space belongs boundary bounded linear functional Cauchy sequence closed linear operator closed linear subspace closure compact operators compact set complete consider constant contains a sphere continuous inverse continuous linear functional continuous map converges convex set denote dense set differential equation disjoint domain E₁ eigenvalue element f₁ F₁(x finite dimensional finite number fixed point follows Fourier Frechet differential functional f graph Hahn-Banach Theorem Hence Hilbert space implicit function theorem inequality internal point L₂ Lemma linear functional defined linear normed space linear subspace linear topological space metric space neighborhood normed linear space origin Problem Proof of Theorem prove R₂ reflexive Riesz satisfying scalar sp(T Suppose three lines theorem topological space uniformly bounded uniformly convex unit sphere valued functions vanishes X₁ x₂ y₁ zero