## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 83

Page 254

Now since u € U there is a finite chain of the form given in [ * ] above in which

successive vectors have non - zero scalar products . Thus by forming the chain

Up , Ug , Uz's V g . it is

Since ...

Now since u € U there is a finite chain of the form given in [ * ] above in which

successive vectors have non - zero scalar products . Thus by forming the chain

Up , Ug , Uz's V g . it is

**seen**that vg is equivalent to vz , and thus that Vp is in V.Since ...

Page 286

Since x * ( % ) converges , it is

that lim S 8 ( s ) } , ( $ ) u ( ds ) = 0 uniformly in n . Since it is assumed for the

present that u ( S ) < ooit is

Since x * ( % ) converges , it is

**seen**from the Vitali - HahnSaks theorem ( III.7.2 )that lim S 8 ( s ) } , ( $ ) u ( ds ) = 0 uniformly in n . Since it is assumed for the

present that u ( S ) < ooit is

**seen**from Theorem III.6.15 that fg is in L , and that ...Page 715

Thus it is

roots of unity , and by Lemma VII.3.7 the same holds for o ( T ) . The remaining

conclusions in Theorems 6 and 7 are then provided exactly as before , since no ...

Thus it is

**seen**from Theorem 5 that all the points of o ( T * ) of unit modulus areroots of unity , and by Lemma VII.3.7 the same holds for o ( T ) . The remaining

conclusions in Theorems 6 and 7 are then provided exactly as before , since no ...

### What people are saying - Write a review

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

### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

### Other editions - View all

### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero