## Linear Operators: Spectral theory |

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Page 898

If we put E ( 8 ) = 0 when d n ( T ) is void , then

from Theorem 1 and

defined spectral measure associated , in

is ...

If we put E ( 8 ) = 0 when d n ( T ) is void , then

**Corollary**4 follows immediatelyfrom Theorem 1 and

**Corollary**IX . 3 . 15 . Q . E . D . 5 DEFINITION . The uniquelydefined spectral measure associated , in

**Corollary**4 , with the normal operator Tis ...

Page 1142

14 . Q . E . D . In what follows , we will use the symbols p and n to denote the

continuous extension to the classes Co of operators of the mappings p and n of

the previous lemma . We will also write t ( p + n ) 2 . We note the following

14 . Q . E . D . In what follows , we will use the symbols p and n to denote the

continuous extension to the classes Co of operators of the mappings p and n of

the previous lemma . We will also write t ( p + n ) 2 . We note the following

**corollary**.Page 1301

Proceeding inductively we see that vk ) ( b ) = 0 , 0 Sk < 2n - 1 . However , as vo

satisfies an equation of order 2n , v , must be identically zero . This contradiction

completes the proof . Q . E . D . 23

Proceeding inductively we see that vk ) ( b ) = 0 , 0 Sk < 2n - 1 . However , as vo

satisfies an equation of order 2n , v , must be identically zero . This contradiction

completes the proof . Q . E . D . 23

**COROLLARY**. Let t be a formal differential ...### What people are saying - Write a review

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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 |

### Common terms and phrases

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