## Linear Operators: General theory |

### From inside the book

Results 1-3 of 33

Page vi

The

The

**present**work is written for the student as well as for the mature mathematician . Much of the text has grown directly out of lectures given by the authors over many years , and the two parts are designed to form suitable texts for a ...Page 285

Thus the

Thus the

**present**theorem is a corollary of Theorem 6.18 . Q.E.D. 8. The Spaces L ( S , E , p ) The spaces L ( S , E , u ) , 1 sp < , have already been studied in Chapter III . In particular it was shown in Theorem III.6.6 that they are ...Page 286

1 discussion of the

1 discussion of the

**present**section covers the space l , as well as the space L ( S , E , u ) . THEOREM . If 1 < p < 0 and 1 / p + 1 / 9 = 1 , there is an isometric isomorphism between L * ( S , E , p ) and L ( S , E , u ) in which ...### 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