## Linear Operators: Spectral theory |

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Page 1378

matrix measure { ê ii } , i , j = 1 , . . . , k of

= 1 , . . . , k ; Pij = 0 , if i > k or j > k . Proof . Suppose that 07 , . . . , Or is a

determining set for T . Then it is evident from

i , j = 1 ...

matrix measure { ê ii } , i , j = 1 , . . . , k of

**Theorem**23 is unique , and Pin = Pijs i , j= 1 , . . . , k ; Pij = 0 , if i > k or j > k . Proof . Suppose that 07 , . . . , Or is a

determining set for T . Then it is evident from

**Theorem**23 that if we define { Pis } ,i , j = 1 ...

Page 1379

{ Ô 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 { ê is } follows immediately . Q . E . D .

27 ...

{ Ô is } is the matrix measure of

**Theorem**23 , the values Pis ( e ) 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 { ê is } follows immediately . Q . E . D .

27 ...

Page 1904

15 remarks on , ( 389 - 392 ) Convergence

on convergence of measures , IV . 9 . 15 ( 316 ) Arzelà

limits , IV . 6 . 11 ( 268 ) Banach

15 remarks on , ( 389 - 392 ) Convergence

**theorems**, IV . 15 Alexandroff**theorem**on convergence of measures , IV . 9 . 15 ( 316 ) Arzelà

**theorem**on continuouslimits , IV . 6 . 11 ( 268 ) Banach

**theorem**for operators into space of measurable ...### What people are saying - Write a review

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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