## 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 Tį and T in

Hilbert space H are said to be unitarily

equation ...

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 Tį and T in

Hilbert space H are said to be unitarily

**equivalent**if they are related by anequation ...

Page 920

unitarily

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

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

Let E and ...

unitarily

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

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

**equivalent**.Let E and ...

Page 1217

If u ( ex ) > 0 for all k , the representation is said to have infinite multiplicity . Two

ordered representations U and U of H relative to T and I respectively , with

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

if u ū ...

If u ( ex ) > 0 for all k , the representation is said to have infinite multiplicity . Two

ordered representations U and U of H relative to T and I respectively , with

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

**equivalent**if u ū ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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