## Linear Operators: General theory |

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Page 247

These steps , with obvious changes in notation , may be used to

These steps , with obvious changes in notation , may be used to

**establish**the isometry when p = 1 or 00. ... from the definition ( 2.26 ) that a Hilbert space is a B - space , but this fact is**established**in the following theorem .Page 403

Using ( i ) and the general theory of Sections III.1 , III.2 , and III.3 , we may now

Using ( i ) and the general theory of Sections III.1 , III.2 , and III.3 , we may now

**establish**an integration theory ( finitely additive ) for functions on y . It turns out , however , that this integration theory is not sufficiently ...Page 463

170 ) independently

170 ) independently

**established**the equivalence of these types of closure without any separability assumptions . ... It is not difficult to**establish**that the regularly convex sets in X * are merely the convex sets which are closed in ...### 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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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