## An introduction to functional analysis |

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### Contents

Convex sets and hyperplanes in vector spaces | 7 |

Linear and sublinear functional | 34 |

Separation of convex sets by hyperplanes | 49 |

Copyright | |

25 other sections not shown

### Common terms and phrases

a-additive absolutely convex associated assume ball Banach algebra Banach space Borel called Cauchy sequence closed subspace compact set compact space consider contains continuous function continuous linear functional converges convex set corresponding countable definition denote dense disjoint elementary integral elementary measure elements equivalent exists fact finite number finite-dimensional fixed following properties following theorem formula Fourier Fredholm functions defined given Hence Hilbert space holds homomorphism hyperplane implies inequality injective internal point interval invertible isometric isomorphism Lebesgue integral Lebesgue measure Lemma let us show linear mapping maximal metric space monomorphism Moreover neighbourhood Noether normed space obtain open set ordered vector space orthogonal positive linear functional Proof Proposition Let real numbers Riesz seminorm Similarly sublinear sublinear functional subset surjective topology unique vector subspace weak type zero