## Linear Operators: Spectral theory |

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Page 890

... then the function E is a resolution of the identity for T and the operational calculus is given by the

... then the function E is a resolution of the identity for T and the operational calculus is given by the

**formula**( vi ) f ( T ) = Sop , ( 2 ) E ( da ) . where the integral is defined as the finite sum L- | ( 2 ; ) E ( 2 ) .Page 1089

The basic properties of the characteristic numbers un ( T ) are stated in the following lemma and corollaries . be nat 2 LEMMA . The characteristic numbers un ( T ) of a compact operator are given by the following

The basic properties of the characteristic numbers un ( T ) are stated in the following lemma and corollaries . be nat 2 LEMMA . The characteristic numbers un ( T ) of a compact operator are given by the following

**formula**: ( 11 L'est ...Page 1363

basis for this

basis for this

**formula**is found in Theorem XII.2.10 which asserts that the projection in the resolution of the identity for T corresponding to ( 1g , 22 ) may be calculated from the resolvent by the**formula**1 E ( ( 17 , 13 ) ) = lim lim ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

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