## Linear Operators: General theory |

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Page 6

It will next be

It will next be

**shown**that P is admissible . The condition ( i ) is vacuously satisfied by P. To prove that P has the property ( ii ) , let x € P. It will be**shown**that if z € A , and > < f ( x ) , then f ( x ) = f ( x ) .Page 156

More direct relationships between set functions and certain B - spaces are explicitly discussed in the next chapter , where it is

More direct relationships between set functions and certain B - spaces are explicitly discussed in the next chapter , where it is

**shown**that the conjugate spaces of some familiar B - spaces may be represented in terms of set functions .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 e Wo , cna is not void . Let æ be the smallest element of cna ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### 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