## Linear Operators: General theory |

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Page 243

**Hilbert space**has been defined by a set of abstract axioms . It is noteworthy that some of the concrete spaces defined above satisfy these axioms ...Page 256

If , however , each of the spaces X , ... , Xn are

If , however , each of the spaces X , ... , Xn are

**Hilbert spaces**then it will ... that X is the uniquely determined**Hilbert space**with scalar product n ...Page 851

... in B - spaces , II.3.4 ( 59 ) discussion of , ( 82–83 ) in F - spaces ... II.3.1 ( 59 ) Orthocomplement of a set in

... in B - spaces , II.3.4 ( 59 ) discussion of , ( 82–83 ) in F - spaces ... II.3.1 ( 59 ) Orthocomplement of a set in

**Hilbert space**, definition , IV.4.3 ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero