## Linear Operators, Part 2 |

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Page 993

Then it

. , Qy is independent of V . Q . E . D . 16 THEOREM . If the bounded measurable

function o has its spectral set consisting of the single point m then , for some ...

Then it

**follows**from what has just been demonstrated that ay , = Qyuv , = Qy , i . e. , Qy is independent of V . Q . E . D . 16 THEOREM . If the bounded measurable

function o has its spectral set consisting of the single point m then , for some ...

Page 996

Since f * q is continuous by Lemma 3 . 1 ( d ) it

that f * ° + 0 . From Lemma 12 ( b ) it is seen that olf * 9 ) Colg ) and from Lemma

12 ( c ) and the equation of = tf it

...

Since f * q is continuous by Lemma 3 . 1 ( d ) it

**follows**from the above equationthat f * ° + 0 . From Lemma 12 ( b ) it is seen that olf * 9 ) Colg ) and from Lemma

12 ( c ) and the equation of = tf it

**follows**that olf * Q ) contains no interior point of o...

Page 1124

Hence ( Exn | 2 = E , x , for each n , so that Exn = EzXn and E = E . That is , Q ( E )

= 4 ( E ) implies E = E . Similarly , Q ( E ) S Q ( E ) implies E s Eq . If En . E are in F

and ( En ) increases to the limit ( E ) , then it

Hence ( Exn | 2 = E , x , for each n , so that Exn = EzXn and E = E . That is , Q ( E )

= 4 ( E ) implies E = E . Similarly , Q ( E ) S Q ( E ) implies E s Eq . If En . E are in F

and ( En ) increases to the limit ( E ) , then it

**follows**from what we have already ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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