## Linear Operators: General theory |

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**follows**readily from the definition of v ( ug ) that v ( un , 6-1 ( E ) ) z v ( 42 , E ) . Conversely , since ( EU EZ ) = $ ( EU ( E2 ) and $ ( E , E2 ) = ° ( E ) ( E2 ) if Ey , E , belong to El , v ( uz , ° ( E ) ) is a nonnegative ...Page 403

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**follows**from the rotational invariance of Un that Mon may be regarded as a measure defined intrinsically in any n - dimensional real Hilbert space H , without reference to any particular coordinate system in that space .Page 714

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**follows**from its definition that Ep is a projection , that ЕРЕр E , Ep = = = 0 , and that I = Ep + Ep . Further T ... is into subspaces invariant under T. Statements ( a ) and ( b )**follow**from the formula for Tm given in Theorem 6.### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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