## Linear Operators: General theory |

### From inside the book

Results 1-3 of 87

Page 262

Since the integral Ss / ( s ) u ( ds ) satisfies the inequality | Ss t ( s ) u ( ds ) < sup || ( s ) [ 0 ( yu , S ) , it is

Since the integral Ss / ( s ) u ( ds ) satisfies the inequality | Ss t ( s ) u ( ds ) < sup || ( s ) [ 0 ( yu , S ) , it is

**clear**that the integral is a continuous linear functional on C ( S ) . The following theorem is a converse to ...Page 282

It is

It is

**clear**that T ( 8 ) CT ( S ) if € < d and that -te T ( 8 ) whenever t e T ( € ) . The function f is said to be almost periodic if it is continuous and if for every ε > 0 there is an L L ( E ) > 0 such that every interval in R of ...Page 292

It is also

It is also

**clear**that if Fi e Eg , then S - F , e Eg , and that if F1 , F2 € Es with F , F , = 0 , then F , UF , € £ g . It follows that E , is a field . If { Fx } is a sequence of disjoint elements of Eg with union F and if E , e & ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

### Common terms and phrases

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