## 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 * < > 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 * < > 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 ( S ) . ... The correspondence % e →Xe , establishes an**isomorphism**t of the field onto the field E , of all open and closed sets in S , , i . e ., t ( EUF ) = t ...

Page 313

Recalling that t is an

isometric

TE ; ) ) = sup & lu ( E ; ) ] = lul , u ( E ) 0 equation 21 ( F ). E | where { E1 , En } is ...

Recalling that t is an

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

**isomorphism**of ba ( S , E ) onto ba ( S , E ) , since \ Tul = sup 2 ( Tu ) (TE ; ) ) = sup & lu ( E ; ) ] = lul , u ( E ) 0 equation 21 ( F ). E | where { E1 , En } is ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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