## 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 ( S ) . 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 ( S ) . Theorem 5.1 shows that there is an isometric

**isomorphism**x ...Page 312

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

7 ( EUF ) ...

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

**isomorphic**with C ( S , ) . ... The correspondence % e → % E , establishes an**isomorphism**t of the field onto the field E , of all open and closed sets in Sy , i.e. ,7 ( EUF ) ...

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The correspondence U : M1 → Ma is an isometric

onto ca ( S1 , A2 ) . ( c ) If E , is in E , then v ( 41 , E1 ) = v ( U ( M1 ) , Ey ) for all Mi

in ba ( S ,, £ ) . PROOF . Recalling that t is an

The correspondence U : M1 → Ma is an isometric

**isomorphism**of ba ( S1 , Ey )onto ca ( S1 , A2 ) . ( c ) If E , is in E , then v ( 41 , E1 ) = v ( U ( M1 ) , Ey ) for all Mi

in ba ( S ,, £ ) . PROOF . Recalling that t is an

**isomorphism**of onto Ej , it is clear ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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