## Linear Operators: General theory |

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Page 114

**Statement**( b ) is clear from the definitions .**Statement**( c ) is evident for u - integrable simple functions ; to prove it in the general case , let In be a sequence of finitely valued u - simple functions which determine g .Page 415

... ( iv ) If CO ( A ) is compact , then CO ( A + B ) = CO ( A ) + CO ( B ) . Proof . The first part of

... ( iv ) If CO ( A ) is compact , then CO ( A + B ) = CO ( A ) + CO ( B ) . Proof . The first part of

**statement**( i ) follows in an elementary fashion from Lemma 1.4 . Lemma 1.4 also shows that co ( A + B ) CCO ( A ) + co ( B ) .Page 447

**Statement**( b ) follows from the inequality a 2f ( x + 2 ( Yi + y2 ) ) 5 k ( x + ayı ) + k ( x + ayz ) .**Statement**( c ) is trivial .**Statement**( d ) follows from the inequality t ( x , y ) +7 ( x , y ) 1 ( x , 0 ) = 0 ) .t ( x ...### 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 | |

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