## Linear Operators: Spectral theory |

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Page 925

16 Let Ni , N2 , . . . 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 Ni , N2 , . . . be a countable

**sequence**of normal operators in H , 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 ebm . Since Mo is countably additive on Bo , Molebn ) = limm

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

...

Since Ueem = e , the

**sequence**{ eembn , m 2 1 } is an increasing**sequence**ofsets whose union is ebm . Since Mo is countably additive on Bo , Molebn ) = limm

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

...

Page 1124

If Ex , E are in F and q ( En ) increases to the limit 9 ( E ) , then it follows from what

we have already proved that En is an increasing

SE . If E . is the strong limit of En , then E . SE and Q ( E ) = Q ( E ) . Thus , it ...

If Ex , E are in F and q ( En ) increases to the limit 9 ( E ) , then it follows from what

we have already proved that En is an increasing

**sequence**of projections and E ,SE . If E . is the strong limit of En , then E . SE and Q ( E ) = Q ( E ) . Thus , it ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

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