## Linear Operators: General theory |

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Page 183

it

E , Conversely , since $ ( E , U EZ ) = $ ( EU $ ( E2 ) and $ ( E , E2 ) = $ ( EZ ) * (

E2 ) if Ej , E , belong to En , v ( u2 , 6 ( E ) ) is a nonnegative additive set function ...

it

**follows**readily from the definition of v ( ug ) that v ( un , 6-4 ( E ) ) 2 v ( um , E ) .E , Conversely , since $ ( E , U EZ ) = $ ( EU $ ( E2 ) and $ ( E , E2 ) = $ ( EZ ) * (

E2 ) if Ej , E , belong to En , v ( u2 , 6 ( E ) ) is a nonnegative additive set function ...

Page 403

It

defined intrinsically in any n - dimensional real Hilbert space H , without

reference to any particular coordinate system in that space . This measure will be

called ...

It

**follows**from the rotational invariance of Mn that Min may garded as a measuredefined intrinsically in any n - dimensional real Hilbert space H , without

reference to any particular coordinate system in that space . This measure will be

called ...

Page 714

It

= Ep + Ep . Further T commutes with Ep and E so this direct sum decomposition is

into subspaces invariant under T. Statements ( a ) and ( b )

It

**follows**from its definition that Ep is a projection , that EpEp = E Ep 0 , and that I= Ep + Ep . Further T commutes with Ep and E so this direct sum decomposition is

into subspaces invariant under T. Statements ( a ) and ( b )

**follow**from the ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

81 other sections not shown

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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