## 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 71

Page 2300

Then , since the collection of

bounded , it is clear from [ * ] that the collection of

; T + P ) , n 2 K , is uniformly bounded . Moreover , Erap ( Elan ; T ) – Elun ; T + P ...

Then , since the collection of

**finite**sums of projections E ( n ; T ' ) is uniformlybounded , it is clear from [ * ] that the collection of

**finite**sums of projections E ( Mn; T + P ) , n 2 K , is uniformly bounded . Moreover , Erap ( Elan ; T ) – Elun ; T + P ...

Page 2333

Hence , in view of the Fubini theorem , the proof of ( a ) will be complete as soon

as the quantity popoo $ $ $ e - mée - mof ( e ) f ( s ) dt ds dm = $ 10 $ 401 ( 9 ) dt

ds do Jo Jo is proved to be

Hence , in view of the Fubini theorem , the proof of ( a ) will be complete as soon

as the quantity popoo $ $ $ e - mée - mof ( e ) f ( s ) dt ds dm = $ 10 $ 401 ( 9 ) dt

ds do Jo Jo is proved to be

**finite**. Since f is in L2 ( 0 , 0 ) , it is sufficient by ...Page 2441

This shows that there exists a

lal ) - n + 1 . Using this inequality and using ( 37 ) , we see that there exists a

constant M " independent of ε such that ( 43 ) 17 6 . + younger og levererar o ...

This shows that there exists a

**finite**absolute constant c ' such that 1 ( a ) c ' ( 1 +lal ) - n + 1 . Using this inequality and using ( 37 ) , we see that there exists a

**finite**constant M " independent of ε such that ( 43 ) 17 6 . + younger og levererar o ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero