## Linear Operators: General theory |

### From inside the book

Results 1-3 of 87

Page 245

Every linear operator on a

Every linear operator on a

**finite**dimensional normed linear space is continuous . Proof . Let { b1 , ... , bn } be a Hamel basis for the**finite**dimensional normed linear space X so that every x in X has a unique representation in the ...Page 290

Now suppose that ( S , E , u ) is o -

Now suppose that ( S , E , u ) is o -

**finite**, and let En be an increasing sequence of measurable sets of**finite**measure whose union is S. Using the theorem for L ( En ) = L ( En , E ( En ) , u ) , we obtain a sequence { gn } of ...Page 849

( See Decomposition ) definition , III.4.3 ( 126 )

( See Decomposition ) definition , III.4.3 ( 126 )

**finite**, III.4.3 ( 126 ) Lebesgue extension of , III.5.18 ( 143 ) as a metric space , II1.7.1 ( 158 ) , III.9.6 ( 169 ) positive , III.4.3 ( 126 ) product , of**finite**number of**finite**...### 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 | |

81 other sections not shown

### Other editions - View all

### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 meaning measure space metric neighborhood norm operator positive measure problem Proc proof properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero