## 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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Page 2010

3 that pl ( Â ( s ) ) = 0 almost everywhere on S . Thus , for almost all s , o

on the spectrum o ( Â ( s ) ) . So , for some set o , in { with eloo ) = e , the function

o

3 that pl ( Â ( s ) ) = 0 almost everywhere on S . Thus , for almost all s , o

**vanishes**on the spectrum o ( Â ( s ) ) . So , for some set o , in { with eloo ) = e , the function

o

**vanishes**on Uses , O ( Â ( s ) ) , and since y is continuous , it also**vanishes**on ...Page 2343

Consequently , if we use Lagrange ' s rule to expand this 2v x 2v determinant by

minors of order v , we find that the expansion contains only two non -

terms . Thus our 2v X 2v determinant may be expressed as P2P , FQ1Q2 , where

...

Consequently , if we use Lagrange ' s rule to expand this 2v x 2v determinant by

minors of order v , we find that the expansion contains only two non -

**vanishing**terms . Thus our 2v X 2v determinant may be expressed as P2P , FQ1Q2 , where

...

Page 2468

Let q be a non - negative function belonging to C ( R ) ,

1 ] , and satisfying Q ( x ) = 9 ( - x ) and Se ola ) da = 1 . For each E > 0 , and each

BEH ' , define 0ef by ( 44 ) Def = s , where gi ( a ) = f : ( a ) , аєey , 9 : ( a ) ...

Let q be a non - negative function belonging to C ( R ) ,

**vanishing**outside [ - 1 , +1 ] , and satisfying Q ( x ) = 9 ( - x ) and Se ola ) da = 1 . For each E > 0 , and each

BEH ' , define 0ef by ( 44 ) Def = s , where gi ( a ) = f : ( a ) , аєey , 9 : ( a ) ...

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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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### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero