## Linear Operators: General theory |

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Page 311

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

x * 4 u ...

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**x * 4 u ...

Page 312

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

t ( EUF ) = t ...

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

**isomorphic**with C ( Si ) . ... The correspondence % e →XE , establishes an**isomorphism**t of the field onto the field £ , of all open and closed sets in Sį , i . e . ,t ( EUF ) = t ...

Page 313

The correspondence U : M2 → Ma is an isometric

ca ( S , , £ % ) . ( c ) If E , is in E , then v ( un , Ey ) = v ( U ( uz ) , E , ) for all My in

ba ( S1 , E1 ) . Proof . Recalling that t is an

The correspondence U : M2 → Ma is an isometric

**isomorphism**of ba ( S , E ) ontoca ( S , , £ % ) . ( c ) If E , is in E , then v ( un , Ey ) = v ( U ( uz ) , E , ) for all My in

ba ( S1 , E1 ) . Proof . Recalling that t is an

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

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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