## Linear Operators: General theory |

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Page 311

PROOF . Consider the closed subspace B ( S , ) 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 , ) 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 ) = t ...

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

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

Page 313

Recalling that t is an

isometric

TE :) ) = sup Elu ( E ; ) ) = lul , [ Σμ ( . ) n where { Ej , ... , En } is an arbitrary partition

...

Recalling that t is an

**isomorphism**of onto E , it is clear that the mapping T is anisometric

**isomorphism**of ba ( S , E ) onto ba ( Sy , Ej ) , since Tul = sup E ( Tu ) (TE :) ) = sup Elu ( E ; ) ) = lul , [ Σμ ( . ) n where { Ej , ... , En } is an arbitrary partition

...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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