## Linear Operators: General theory |

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Page 140

An

An

**interval**is a set of points in the extended real number system which has one of the forms : [ a , b ] = { sa Sssb } ... The number a is called the left end point and b the right end point of any of these**intervals**.Page 141

3 i = ni + 1 The argument may be repeated by defining Ez = choosing appropriate points in the

3 i = ni + 1 The argument may be repeated by defining Ez = choosing appropriate points in the

**interval**( c , c + Eg ] . By induction , it is clear that for every integer k = 1 , 2 , ... , there are points a ;, bi with c < an Sbne S ..Page 283

Since an almost periodic function f is continuous , the function \ | ( s ) has a maximum K on the

Since an almost periodic function f is continuous , the function \ | ( s ) has a maximum K on the

**interval**o 5 x SL ( 1 ) . Let æ be an arbitrary real number and choose te T ( 1 , f ) in the**interval**- « sts - + L ( 1 ) .### 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