## Linear Operators: General theory |

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Page 140

An

the forms : [ a , b ] = { sa Es sb } , ( a , b ) = { sa Es < b } , ( a , b ] ... The number a is

called the left end point and b the right end point of any of these

An

**interval**is a set of points in the extended real number system which has one ofthe forms : [ a , b ] = { sa Es sb } , ( a , b ) = { sa Es < b } , ( a , b ] ... The number a is

called the left end point and b the right end point of any of these

**intervals**.Page 141

San , + 1 bn + 1 c + en , = an , and such that \ ( bi ) - f ( a ; ) ) > d . i = + 1 The

argument may be repeated by defining Ez = an , - c and choosing appropriate

points in the

1 , 2 ...

San , + 1 bn + 1 c + en , = an , and such that \ ( bi ) - f ( a ; ) ) > d . i = + 1 The

argument may be repeated by defining Ez = an , - c and choosing appropriate

points in the

**interval**( c , c + ez ] . By induction , it is clear that for every integer k =1 , 2 ...

Page 283

The proof will require the following two lemmas . 3 LEMMA . An almost periodic

function is bounded . PROOF OF LEMMA 3 . Since an almost periodic function f is

continuous , the function ( s ) has a maximum K on the

The proof will require the following two lemmas . 3 LEMMA . An almost periodic

function is bounded . PROOF OF LEMMA 3 . Since an almost periodic function f is

continuous , the function ( s ) has a maximum K on the

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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