## 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 61

Page 1986

Hence , to complete the proof of the theorem it suffices to

formula ( 5 ) . By considering the integral as an iterated integral , it is seen that it

suffices to

Hence , to complete the proof of the theorem it suffices to

**establish**the inversionformula ( 5 ) . By considering the integral as an iterated integral , it is seen that it

suffices to

**establish**( 5 ) in the case N = 1 . In this case ... may be**established**by.Page 2212

We next

establishes ( viii ) . We now

fz ( a ) = fw ( ) on 0 , = ow , equation ( ix ) will be

...

We next

**establish**the equation ( viii ) ffz = f : Xo ( f ) , FEB . To prove this , let g ...establishes ( viii ) . We now

**establish**the relation ( ix ) f ( a ) = fy ( a ) , λε ... Thus iffz ( a ) = fw ( ) on 0 , = ow , equation ( ix ) will be

**established**. Hence we may and...

Page 2234

... contained in U and such that E ( Un = 1 en ) = 1 . Then F ( U = 1 ( n ) = 1 also .

Let u be in E ( e ) X and let x be in D ( f ( T | E ( e ) x ) ) . Then by Definition 8 ,

since ( ii ) has already been

... contained in U and such that E ( Un = 1 en ) = 1 . Then F ( U = 1 ( n ) = 1 also .

Let u be in E ( e ) X and let x be in D ( f ( T | E ( e ) x ) ) . Then by Definition 8 ,

since ( ii ) has already been

**established**for bounded Borel sets with closures ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 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 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