## Linear Operators: General theory |

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Page 183

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**follows**readily from the definition of v ( ug ) that v ( uz , 6-1 ( E ) ) 2 v ( ua , E ) . Conversely , since $ ( EU Eg ) = $ ( EU ° ( E ) and $ ( E_E2 ) ...Page 403

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

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**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 ( 0 ) O only ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero