## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 898

If we put E ( S ) = 0 when d n o T ) is void , then

If we put E ( S ) = 0 when d n o T ) is void , then

**Corollary**4 follows immediately from Theorem 1 and**Corollary**IX.3.15 . Q.E.D. 5 DEFINITION . The uniquely defined spectral measure associated , in**Corollary**4 , with the normal ...Page 1142

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**COROLLARY**. ( a ) The mapping T is a bounded map of C , into Cp , 1 < p < 0 . ( b ) If His anti - Hermitian , then the anti - Hermitian part of tH is nH . ( c ) TH leaves invariant the range of each of the projections Ex of Theorem 5 ...Page 1301

However , as vo satisfies an equation of order 2n , v , must be identically zero . This contradiction completes the proof . Q.E.D. 23

However , as vo satisfies an equation of order 2n , v , must be identically zero . This contradiction completes the proof . Q.E.D. 23

**COROLLARY**. Let t be a formal differential operator of order n on an interval I with end points a ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

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