## 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 ...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 complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero