## 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 ...Page 415

The first part of

The first part of

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

**Statement**( b ) follows from the inequality a 2 / ( x + ( Yi + y2 ) ) = k ( x + ayı ) + k ( x + ayz ) . 2**Statement**( c ) is trivial .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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### Common terms and phrases

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