## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 919

Section X.4 ) that unitarily

THEOREM . Two bounded normal operators in a separable Hilbert space H are

unitarily

...

Section X.4 ) that unitarily

**equivalent**operators have identical properties in H. 12THEOREM . Two bounded normal operators in a separable Hilbert space H are

unitarily

**equivalent**if and only if the corresponding ordered representations of H...

Page 920

unitarily

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

Lzlēm ) relative to T. It will follow from Theorem 10 that U and ✓ are

Let E and Ể ...

unitarily

**equivalent**, i.e. , that T = VTV - 1 where Vis unitary . Under thisassumption it will be shown that there is an ordered representation of Honto =

Lzlēm ) relative to T. It will follow from Theorem 10 that U and ✓ are

**equivalent**.Let E and Ể ...

Page 1217

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

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

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

if u ħ and ...

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

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

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

**equivalent**if u ħ and ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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