## 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**x * 4 u between B * ( S , E ) and ba ( S , E ) , which is determined by the equation 2 * XE = u ( E ) ...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 ) . Then the space S , is uniquely determined to within a ...Page 313

The correspondence U : My → Ma is an isometric

The correspondence U : My → Ma is an isometric

**isomorphism**of ba ( Si , Ey ) onto ca ( Si , ) . ( c ) If E , is in £ then v ( uz , Eq ) = v ( U ( M ) ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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