## Linear Operators: General theory |

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Page 67

A closed linear manifold in a

A closed linear manifold in a

**reflexive**B - space is reflerive . Proof . Let y be a closed linear manifold in the**reflexive**space X. Let 5 : x * y * be defined by the equation $ ( x * ) y = x * y , y e Y. Clearly 15 ( x * ) = \ * ...Page 72

Is the result true if X is not

Is the result true if X is not

**reflexive**? I 19 If X is a**reflexive**B - space , and 3 is a closed subspace of X , show , using Exercise 18 , that both 3 and X 3 are**reflexive**. ? 20 If X is a B - space , with 3 CX , and both 3 and X / 3 ...Page 88

**Reflexivity**. The fact that the natural isomorphism of a B - space X into its second conjugate is isometric was proved by Hahn [ 3 ; p . ... He used the term regular to describe what we , following Lorch [ 2 ] , have called**reflexive**.### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero