## Linear Operators, Part 2 |

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Page 925

16 Let N1 , N , , . . . be a countable

commuting with each other . Show that there exists a single Hermitian operator T

such that each N , is a Borel function of T . ( Hint : Use Theorem 2 . 1 and

Exercise 15 ) .

16 Let N1 , N , , . . . be a countable

**sequence**of normal operators in ý , allcommuting with each other . Show that there exists a single Hermitian operator T

such that each N , is a Borel function of T . ( Hint : Use Theorem 2 . 1 and

Exercise 15 ) .

Page 959

Since Ueem = e , the

sets whose union is ebn . Since Mo is countably additive on Boy Molebn ) = limm

Moleembn ) 2k , and so for some m , Moleem ) 2 Ho ( eemba ) > k - € . This shows

...

Since Ueem = e , the

**sequence**{ eembno m 2 1 } is an increasing**sequence**ofsets whose union is ebn . Since Mo is countably additive on Boy Molebn ) = limm

Moleembn ) 2k , and so for some m , Moleem ) 2 Ho ( eemba ) > k - € . This shows

...

Page 1124

Hence , if we choose a countable set { E ; } CF such that { 9 ( E ; ) } is dense in the

range of the function g , then each E in F is the limit either of an increasing or of a

decreasing

Hence , if we choose a countable set { E ; } CF such that { 9 ( E ; ) } is dense in the

range of the function g , then each E in F is the limit either of an increasing or of a

decreasing

**sequence**of projections in F . We shall show below that there ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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