## Linear Operators: General theory |

### From inside the book

Results 1-3 of 83

Page 4

If A is an infinite set of real numbers , then the symbol lim sup A

infimum of all numbers b with the property that only a ... In particular , if A is a

sequence { an } then lim sup A and lim inf A are usually

lim inf an ...

If A is an infinite set of real numbers , then the symbol lim sup A

**denotes**theinfimum of all numbers b with the property that only a ... In particular , if A is a

sequence { an } then lim sup A and lim inf A are usually

**denoted**by lim sup ay )lim inf an ...

Page 103

For an example of such a function , let S = [ 0 , 1 ) and be the field of finite unions

of intervals I = ( a , b ) , o Sa < b < 1 , with u ( I ) = b -- a as in Section 1. Let R

p ...

For an example of such a function , let S = [ 0 , 1 ) and be the field of finite unions

of intervals I = ( a , b ) , o Sa < b < 1 , with u ( I ) = b -- a as in Section 1. Let R

**denote**the set of rational points in S. For r p / q e R in lowest terms , we define F (p ...

Page 142

Throughout the proof the symbol E with or without subscripts will

E , the symbol M with or without subscripts will

) = 0 , and N with or without subscripts will

Throughout the proof the symbol E with or without subscripts will

**denote**a set inE , the symbol M with or without subscripts will

**denote**a set in E for which v ( u , M) = 0 , and N with or without subscripts will

**denote**a subset of a set M. To see ...### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

### 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