## Linear Operators: Spectral theory |

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Page 925

a 20 16 Let N , N2 , ... be a countable

a 20 16 Let N , N2 , ... be a countable

**sequence**of normal operators in , all commuting with each other . Show that there exists a single Hermitian operator T such that each Nx is a Borel function of T. ( Hint : Use Theorem 2.1 and ...Page 959

Since Ueem = e , the

Since Ueem = e , the

**sequence**{ eembn , m 1 } is an increasing**sequence**of sets whose union is ebm . Since Mo is countably additive on Bo , Molebn ) = lim , n Moleembn ) 2 k , and so for some m , Mo ( eem ) Holeembn ) > k - e .Page 1124

If En , E are in F and 9 ( En ) increases to the limit q ( E ) , then it follows from what we have already proved that En is an increasing

If En , E are in F and 9 ( En ) increases to the limit q ( E ) , then it follows from what we have already proved that En is an increasing

**sequence**of projections and E , SE . If EQ is the strong limit of En , then E. SE and q ( E ) = Q ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

44 other sections not shown

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