## Linear Operators: General theory |

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Page 311

Theorem 5.1 shows that there is an isometric

Theorem 5.1 shows that there is an isometric

**isomorphism**æ * \ between B * ( S , E ) and ba ( S , E ) , which is determined by the equation x * XE = 4 ( E ) , E € £ . Thus , since B ( S , E ) is equivalent to C ( S ) , ba ( S , E ) is ...Page 312

Let S , be a compact Hausdorff space such that B ( S , E ) is isometrically

Let S , be a compact Hausdorff space such that B ( S , E ) is isometrically

**isomorphic**with C ( S ) . ... The correspondence Xe + % E , establishes an**isomorphism**7 of the field & onto the field of all open and closed sets in S ...Page 313

The correspondence U : My → Ma is an isometric

The correspondence U : My → Ma is an isometric

**isomorphism**of ba ( S1 , Ey ) onto ca ( Sı , E2 ) . ( c ) If E , is in £ , then v ( un , Ey ) = v ( U ( M ) , E ) for all M , in ba ( S1 , £ ; ) . Proof .### 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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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