## Linear Operators, Part 2 |

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Page 889

... a normal operator T in Hilbert space H determines a spectral measure which is defined on the Boolean algebra B of all

... a normal operator T in Hilbert space H determines a spectral measure which is defined on the Boolean algebra B of all

**Borel**sets in the plane and which ...Page 913

Let E be the spectral resolution for T and let vn ( e ) = ( E ( e ) yn , yn ) for each

Let E be the spectral resolution for T and let vn ( e ) = ( E ( e ) yn , yn ) for each

**Borel**set e . Using the Lebesgue decomposition theorem ( III.4.14 ) ...Page 1900

... 1.12.1 ( 41 )

... 1.12.1 ( 41 )

**Borel**field of sets , definition , III.5.10 ( 137 )**Borel**function , X.1 ( 891 )**Borel**measurable function , X.I ( 891 )**Borel**( or**Borel**...### 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