## Linear Operators: Spectral theory |

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Page 875

It will also be shown that this

preserving the operation of involution . This basic result , which is due to Gelfand

and Naïmark , will find many applications in the next two chapters . 3 LEMMA . If

X is a ...

It will also be shown that this

**isomorphism**is a * -**isomorphism**, i . e . , onepreserving the operation of involution . This basic result , which is due to Gelfand

and Naïmark , will find many applications in the next two chapters . 3 LEMMA . If

X is a ...

Page 878

There is one isometric * -

single out . In the notation of the preceding proof the * -

- ) ) of B * ( x ) onto C ( 0 ( x ) ) has the property that x corresponds to the function

...

There is one isometric * -

**isomorphism**of B * ( x ) onto C ( o ( x ) ) that we wish tosingle out . In the notation of the preceding proof the * -

**isomorphism**y + y ( x - 1 (- ) ) of B * ( x ) onto C ( 0 ( x ) ) has the property that x corresponds to the function

...

Page 1373

of L ( 1 , { Pi } ) into L2 ( 1 , { i } ) and an isometric

into L2 ( 1 , Ais } ) . Since { ajj ( a ) } and { bis ( a ) } are inverse matrices , it follows

readily that AB = BA = I . Thus , A and B are isometric

of L ( 1 , { Pi } ) into L2 ( 1 , { i } ) and an isometric

**isomorphism**of L , ( 4 , { Wix } )into L2 ( 1 , Ais } ) . Since { ajj ( a ) } and { bis ( a ) } are inverse matrices , it follows

readily that AB = BA = I . Thus , A and B are isometric

**isomorphisms**onto all of ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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