## Linear Operators: Spectral theory |

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Page 993

Then it

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

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

Page 996

1 ( d ) it

seen that olf * 9 ) Colo ) and from Lemma 12 ( c ) and the equation of = tf it

that o ( f * Q ) contains no interior point of o ( p ) . Hence olf * ) is a closed subset ...

1 ( d ) it

**follows**from the above equation that f * 9 + 0 . From Lemma 12 ( b ) it isseen that olf * 9 ) Colo ) and from Lemma 12 ( c ) and the equation of = tf it

**follows**that o ( f * Q ) contains no interior point of o ( p ) . Hence olf * ) is a closed subset ...

Page 1450

Part ( a )

12 , and ... Q . E . D . A number of additional criteria of this sort for the second

order operator 2 - ( ) * + 960 )

6 .

Part ( a )

**follows**immediately from Theorem 9 . Part ( b )**follows**from Corollary 6 .12 , and ... Q . E . D . A number of additional criteria of this sort for the second

order operator 2 - ( ) * + 960 )

**follow**from the corresponding theorems of Section6 .

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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