## Introduction to the Theory of Hilbert Spaces, Volume 1 |

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### Contents

Foreword Table of Contents Chapter I | 1 |

Notions of vector calculus | 4 |

Abstract vector spaces | 5 |

Copyright | |

26 other sections not shown

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### Common terms and phrases

Banach space belongs bilinear form F(u,v 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 continuous transformation converge strongly convex coordinates corresponding bilinear decreasing sequence define denote dimension direct sum distance domain equal exists fact finite number formula given gives graph hand hermitian Hilbert space Hull Hull2 immediately verified implies intersection interval 0;l inverse isomorphism limit linear combination linear transformation linearly independent linearly independent vectors metric space normed vector space notion obtain one-dimensional one-to-one correspondence open sets orthogonal sum paragraph 24 plane positive definite proof proper norm prove pseudo-norm quadratic form quadratic form F(u,u quotient space real numbers real space reduced angle representative subspace satisfies scalar product sequence of numbers sequential space strong convergence subset vll2 weak convergence zero element