## Linear Operators, Part 2 |

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Page 919

Section X.4 ) that unitarily

Section X.4 ) that unitarily

**equivalent**operators have identical properties in H. 12 THEOREM . Two bounded normal operators in a separable Hilbert space H ...Page 920

unitarily

unitarily

**equivalent**, i.e. , that Ť = VTV - 1 where V is unitary . Under this assumption it will be shown that there is an ordered representation of H onto ...Page 1217

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

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

**equivalent**if u ħ and ule , 4ěn ) = 0 ) = ùle , dēm ) for n = 1 , 2 , .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero