## Linear Operators: Spectral theory |

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Page 1378

Suppose that 01 , . . . , 07 is a determining set for T . Then it is evident from

, k , Pijle ) = 0 if i > k or j > k , we get a matrix measure { Pis } which by Corollary

21 ...

Suppose that 01 , . . . , 07 is a determining set for T . Then it is evident from

**Theorem**23 that if we define { pish , i , j = 1 , . . . , n , by Pijle ) = Pijle ) , i , j = 1 , . . ., k , Pijle ) = 0 if i > k or j > k , we get a matrix measure { Pis } which by Corollary

21 ...

Page 1379

{ ź is } is the matrix measure of

determined for each e C N . Since 1 is the union of a sequence of neighborhoods

of the same type as N , the uniqueness of fis } follows immediately . Q . E . D . 27 ...

{ ź is } is the matrix measure of

**Theorem**23 , the values Pile ) are uniquelydetermined for each e C N . Since 1 is the union of a sequence of neighborhoods

of the same type as N , the uniqueness of fis } follows immediately . Q . E . D . 27 ...

Page 1904

15 remarks on , ( 389 - 392 ) Convergence

continuous limits , IV . 6 . 11 ( 268 ) Banach

measurable ...

15 remarks on , ( 389 - 392 ) Convergence

**theorems**, . IV . 15 Alexandroff**theorem**on convergence of measures , IV . 9 . 15 ( 316 ) Arzelą**theorem**oncontinuous limits , IV . 6 . 11 ( 268 ) Banach

**theorem**for operators into space ofmeasurable ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 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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