## 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 * < > u between B * ( S , E ) and ba ( S , E ) , which is determined by the equation x * XE = u ( E ) , E € £ . Thus , since B ( S , E ) is equivalent to C ( S ) , ba ( S ...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 → Xe , establishes an**isomorphism**t of the field onto the field Ey of all open and closed sets in Sį ...Page 313

The correspondence U : M → My is an isometric

The correspondence U : M → My is an isometric

**isomorphism**of ba ( S1 , Ey ) onto ca ( S1 , E2 ) . ( c ) If E , is in E , then v ( M , EZ ) = v ( U ( u ) , E , ) for all My in ba ( S1 , E1 ) . PROOF . Recalling that t is an**isomorphism**...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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