## Linear Operators: General theory |

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Page 436

6 Let X be a B - space , and X , a

6 Let X be a B - space , and X , a

**subspace**of X. Show that the X * topology of X , is the same as the relative X * topology of X. 7 Let X be a linear space , and I a total**subspace**of x * . Show that a set A Ç X is T - bounded if and ...Page 504

Then there exists a closed separable

Then there exists a closed separable

**subspace**y of X such that M is equivalent to a**subspace**of y * . Proof . Let { w * } be a countable dense subset of M , and let { xmn } , m , n = 1 , 2 , ... , belong to X and satisfy the relations ...Page 513

16 If Y is a closed

16 If Y is a closed

**subspace**of a B - space and N is a finite dimensional**subspace**, then Y O N is a closed**subspace**. If Y O N is a closed**subspace**, and N is finite dimensional , it does not follow that Y is closed .### 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