## Linear Operators: Spectral theory |

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Page 925

16 Let N1, N2, ... be a countable

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

such that each No is a Borel function of T. (Hint: Use Theorem 2.1 and Exercise

15).

16 Let N1, N2, ... be a countable

**sequence**of normal operators in S5, allcommuting with each other. Show that there exists a single Hermitian operator T

such that each No is a Borel function of T. (Hint: Use Theorem 2.1 and Exercise

15).

Page 959

Since Uee, = e, the

whose union is eb, . Since uo is countably additive on 30, uo(eb,) = limm u0(een

ba) > k, and so for some m, u0(een) > uo(ee, b, ) > k—e. This shows that the set ...

Since Uee, = e, the

**sequence**{ee,b, m > 1} is an increasing**sequence**of setswhose union is eb, . Since uo is countably additive on 30, uo(eb,) = limm u0(een

ba) > k, and so for some m, u0(een) > uo(ee, b, ) > k—e. This shows that the set ...

Page 1124

That is, q (E) = p(E1) implies E = E1. Similarly, q.(E) < p(E1) implies E s E1. If E, ,

E are in 37 and q(E.) increases to the limit q(E), then it follows from what we have

already proved that E, is an increasing

That is, q (E) = p(E1) implies E = E1. Similarly, q.(E) < p(E1) implies E s E1. If E, ,

E are in 37 and q(E.) increases to the limit q(E), then it follows from what we have

already proved that E, is an increasing

**sequence**of projections and E, s E. If Es, ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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