## Linear Operators: General theory |

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Page 311

Theorem 5 . 1 shows that there is an isometric

S , E ) and ba ( S , E ' ) , which is determined by the equation x * % e = u ( E ) , E €

E . Thus , since B ( S , E ) is equivalent to C ( Si ) , ba ( S , E ) is ...

Theorem 5 . 1 shows that there is an isometric

**isomorphism**x * 4 u between B * (S , E ) and ba ( S , E ' ) , which is determined by the equation x * % e = u ( E ) , E €

E . Thus , since B ( S , E ) is equivalent to C ( Si ) , ba ( S , E ) is ...

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

Page 313

The correspondence U : My → My is an isometric

ca ( Sı , Ez ) . ( c ) If E , is in £ , then v ( uz , EZ ) = v ( U ( uz ) , E , ) for all My in ba (

Sį , & ; ) . PROOF . Recalling that t is an

The correspondence U : My → My is an isometric

**isomorphism**of ba ( Sı , £ ) ontoca ( Sı , Ez ) . ( c ) If E , is in £ , then v ( uz , EZ ) = v ( U ( uz ) , E , ) for all My in ba (

Sį , & ; ) . PROOF . Recalling that t is an

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

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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