## Linear Operators: General theory |

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[ Q , ... , n ] determined by the equation x * n p ? x * x = Σαβ :, { Pi } eln i = 1 is an

[ Q , ... , n ] determined by the equation x * n p ? x * x = Σαβ :, { Pi } eln i = 1 is an

**isometric**isomorphism of ( 1 % ) * onto 2m . Proof . It is clear that the mapping is an isomorphism . To see that it is also an**isometric**map we ...Page 313

The correspondence U : M → My is an

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 ...Page 442

Hence 2 ( Q ) is compact , and 2 is a homeomorphism . Q.E.D. 8 THEOREM . ( Banach - Stone ) Let Q and R be compact Hausdorff spaces , and let T be an

Hence 2 ( Q ) is compact , and 2 is a homeomorphism . Q.E.D. 8 THEOREM . ( Banach - Stone ) Let Q and R be compact Hausdorff spaces , and let T be an

**isometric**isomorphism between C ( Q ) and C ( R ) .### 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