## Linear Operators, Part 2 |

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Page 925

a 20 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 ) ...

a 20 16 Let Ni , N2 , ... 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

prove the uniqueness of the limit it will suffice to show that if Molebn ) 2k for some

n , then , for every e > 0 , Mo ( eem ) > k- € for some m . Since Ueem = e , the

ebm .

prove the uniqueness of the limit it will suffice to show that if Molebn ) 2k for some

n , then , for every e > 0 , Mo ( eem ) > k- € for some m . Since Ueem = e , the

**sequence**{ eembn , m 2 1 } is an increasing**sequence**of sets whose union isebm .

Page 1124

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

we have already proved that En is an increasing

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

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

we have already proved that En is an increasing

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

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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