## Linear Operators: General theory |

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14

14

**COROLLARY**. For every x + 0 in a normed linear space X , there is an x * e X * with | æ * | = l and æ * x = 1xl . PROOF . Apply Lemma 12 with Y = 0.Page 188

The best known example of Theorem 2 and its

The best known example of Theorem 2 and its

**Corollary**6 is obtained by taking ( Si , Ei , Mi ) to be the Borel - Lebesgue measure on the real line for i n .Page 662

2

2

**COROLLARY**. When the strong limit E = lim , A ( n ) exists it is a projection of x upon the manifold { x | Tx = x } of fixed points of T. The ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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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