## Linear Operators: General theory |

### From inside the book

Results 1-3 of 79

Page 245

It was

It was

**shown**in the proof of Lemma 1 that da , i = 1 , ... , n , depends continuously upon x . Thus if U is a linear operator on X it is seen that Ux = Q , Ub , t ... ta , Ubn is also continuous in x . Q.E.D. 5 THEOREM .Page 335

It will first be

It will first be

**shown**that W satisfies the hypothesis of Zorn's lemma . To do this we let W. be a totally ordered subset of W ( I.22 ) and let c CUW .. Then , for some a € Wocna is not void . Let æ be the smallest element of cna and ...Page 479

It only remains to be

It only remains to be

**shown**that TX = Y. If ye Y and y ¢ TX , there is ( II.3.13 ) a y * in Y * with y * # 0 , y * T = T * y * = 0. This contradicts the assumption that T * is one - to - one , and proves the lemma .### 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