## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Results 1-3 of 67

Page 1979

Every operator A in AP is the strong limit of a sequence of spectral operators .

PROOF . Let Sk and Ek be as in the proof of the theorem and let Âx ( s ) = Â ( s ) ,

se SK , = 0 , 8€ SK , so that Âx is in û ” . The

) ...

Every operator A in AP is the strong limit of a sequence of spectral operators .

PROOF . Let Sk and Ek be as in the proof of the theorem and let Âx ( s ) = Â ( s ) ,

se SK , = 0 , 8€ SK , so that Âx is in û ” . The

**corresponding**operator Ax = SS Â ( s) ...

Page 2292

... eigenvectors of T

the idempotent function of T

near do and zero elsewhere near the spectrum of T and near infinity , then E ( No

) ...

... eigenvectors of T

**corresponding**to the eigenvalue do . If Eldo ; T ) = E ( 20 ) isthe idempotent function of T

**corresponding**to the analytic function which is onenear do and zero elsewhere near the spectrum of T and near infinity , then E ( No

) ...

Page 2305

8 , 0 ( L ) is the set of numbers in = ( n tæt B + 1 ) ( n + & + B ) , and each

eigenspace

immediately from Corollary 9 that L + B is a spectral operator for each bounded

operator ...

8 , 0 ( L ) is the set of numbers in = ( n tæt B + 1 ) ( n + & + B ) , and each

eigenspace

**corresponding**to these eigenvalues is one - dimensional . It followsimmediately from Corollary 9 that L + B is a spectral operator for each bounded

operator ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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