## 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

Thus , it

with limit 9 ( E ) , then E , has the strong limit E . We may show in exactly the same

way that if Q ( En ) is decreasing with the limit q ( E ) , then En has the strong limit

...

Thus , it

**follows**as above that Em = E . This proves that if q ( En ) is increasingwith limit 9 ( E ) , then E , has the strong limit E . We may show in exactly the same

way that if Q ( En ) is decreasing with the limit q ( E ) , then En has the strong limit

...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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