## Linear Operators: Spectral theory |

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Page 919

The second assertion is evident from the definition of U. Q.E.D. In connection with

the following theorem it should be recalled that two operators T , and T , in Hilbert

space H are said to be unitarily

The second assertion is evident from the definition of U. Q.E.D. In connection with

the following theorem it should be recalled that two operators T , and T , in Hilbert

space H are said to be unitarily

**equivalent**if they are related by an equation T ...Page 920

unitarily

assumption it will be shown that there is an ordered representation of H onto ma ,

Lylēn , ū ) relative to T. It will follow from Theorem 10 that U and Ū are

.

unitarily

**equivalent**, i.e. , that Ť = VTV - 1 where V is unitary . Under thisassumption it will be shown that there is an ordered representation of H onto ma ,

Lylēn , ū ) relative to T. It will follow from Theorem 10 that U and Ū are

**equivalent**.

Page 1217

Two ordered representations U and Ở of H relative to T and † respectively , with

measures u and ï , and multiplicity sets { en } and { en } will be called

u ħ and ule , 4ěn ) = 0 ) = ùle , dēm ) for n = 1 , 2 , .... 16 THEOREM . A separable

...

Two ordered representations U and Ở of H relative to T and † respectively , with

measures u and ï , and multiplicity sets { en } and { en } will be called

**equivalent**ifu ħ and ule , 4ěn ) = 0 ) = ùle , dēm ) for n = 1 , 2 , .... 16 THEOREM . A separable

...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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