## Linear Operators: General theory |

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Page 311

PROOF . Consider the closed subspace B ( S , E ) of B ( S ) . According to

Theorems 6.18 and 6.20 there is a compact Hausdorff space S , such that B ( S ,

E ) is equivalent to C ( $ ) . Theorem 5.1 shows that there is an isometric

PROOF . Consider the closed subspace B ( S , E ) of B ( S ) . According to

Theorems 6.18 and 6.20 there is a compact Hausdorff space S , such that B ( S ,

E ) is equivalent to C ( $ ) . Theorem 5.1 shows that there is an isometric

**isomorphism**æ ...Page 312

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

EUF ) = t ...

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

**isomorphic**with C ( Sy ) . ... The correspondence % E → Xe , establishes an**isomorphism**T of the field onto the field of all open and closed sets in Sy , i.e. , T (EUF ) = t ...

Page 313

The correspondence U : 11 → Hy is an isometric

ca ( S , E , ) . ( c ) If E , is in E , then v ( un , E , ) = v ( U ( 41 ) , E , ) for all M1 in ba (

S1 , E ) . Proof . Recalling that t is an

The correspondence U : 11 → Hy is an isometric

**isomorphism**of ba ( S , E ) ontoca ( S , E , ) . ( c ) If E , is in E , then v ( un , E , ) = v ( U ( 41 ) , E , ) for all M1 in ba (

S1 , E ) . Proof . Recalling that t is an

**isomorphism**of E onto Ej , it is clear that ...### 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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