Introduction to the Theory of Hilbert SpacesReasearch [sic] Foundation, 1950 - Hilbert space |
Contents
Foreword | 1 |
CauchySchwarz and Minkowskis inequalities | 19 |
Linear subspaces and related topics | 25 |
Copyright | |
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Common terms and phrases
Banach space belongs bounded called Cauchy sequence Cauchy-Schwarz inequality classes of equivalence clearly closed set closed subspace closure complex numbers complex space condition Consequently consider contains continuous functions converge strongly convex coordinates define denote dimension direct sum distance domain elements of H equal exists fact finite number formula Gramm's determinant H₁ Hilbert space implies infinite sequences intersection interval 0;1 isomorphism limit linear combination linear transformation linearly independent linearly independent vectors llull means metric space norm in H normed vector space notion obtain one-dimensional one-to-one correspondence open sets orthogonal sum orthonormal P₁ paragraph plane positive definite proof prove pseudo-norm quadratic form quadratic form F(u quotient space real space representative subspace satisfies scalar product sequential space space H strong convergence subsequence subset subspace H subspace of H u₁ vllČ weak convergence weakly zero element