## Linear Operators: General theory |

### From inside the book

Results 1-3 of 8

Page 326

Let 8x and nk have the same

Let 8x and nk have the same

**meaning**as in the previous paragraph . Since each fk is u - integrable it follows from Egoroff's theorem ( III.6.12 ) and the second paragraph of the proof of Theorem III.2.22 that there is a simple function ...Page 377

... ( F3 ) 13.17 9.5 13.22 13.25 Weak Convergence to x 13.23 13.24 13.18 9.15 13.24 Y Convergence in X Y *

... ( F3 ) 13.17 9.5 13.22 13.25 Weak Convergence to x 13.23 13.24 13.18 9.15 13.24 Y Convergence in X Y *

**meaning**. less meaningless ( F5 ) Miscellaneous Properties 9.11 ( b ) III.7.5 III.7.6 13.50 13.76 13.77 ( F5 ) III.7.5 III.7.6 .Page 534

( S , E , u ) has a known

( S , E , u ) has a known

**meaning**; in the course of this section we will also see how to define Lo ( S , E , M ) . For 1 spsco , L , is a B - space , but for 0 < p < 1 , L , is merely an F - space ( cf.### 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