## Linear Operators: General theory |

### From inside the book

Results 1-3 of 89

Page 269

Since the integral [ st ( s ) u ( ds ) satisfies the inequality IJsH ( 9 ) u ( ds ) ) = sup | t ( s ) vlu , S ) , it is

Since the integral [ st ( s ) u ( ds ) satisfies the inequality IJsH ( 9 ) u ( ds ) ) = sup | t ( s ) vlu , S ) , it is

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

It is

It is

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

It is

It is

**clear**that if F , and F , are elements of E3 , then F F , € Eg . It is also**clear**that if F , € Ez , then S - F , € Ez , and that if F1 , F2 € Eg with F , F2 = $ , then Fi UF , € Eg . It follows that E , is a field .### 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 |

quences | 26 |

Copyright | |

80 other sections not shown

### Other editions - View all

### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero