## Linear Operators: General theory |

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Page 403

It

It

**follows**from the rotational invariance of un that Un may be regarded as a measure defined intrinsically in any n - dimensional real Hilbert space H ...Page 576

It

It

**follows**from Theorem 10 that the map o → E ( 0 ) is a homeomorphism . To verify that it is an isomorphism , it will suffice to show that E ( q ) = 0 ...Page 689

The desired conclusion

The desired conclusion

**follows**from Corollary II.3.13 . Q.E.D. 3 COROLLARY . In a reflexive space , the averages A ( a ) are strongly convergent if they are ...### 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