## 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 2066

Thus c is a

multiplicative group of the unit circle in the complex plane . A well known

elementary result then gives the existence of a uniquely determined point s = s (

h ) in RN with ...

Thus c is a

**continuous**homomorphism of the additive group RN onto themultiplicative group of the unit circle in the complex plane . A well known

elementary result then gives the existence of a uniquely determined point s = s (

h ) in RN with ...

Page 2443

1 p 24 THEOREM . Let 1 sp < , and let Lp [ 0 , 1 ] be the space of all complex

valued , Borel - Lebesgue measurable functions defined in [ 0 , 1 ] and satisfying {

$ 15 ( 2 ) | P dx } " * = \ s \ < . Let g ( x , y ) be defined and

triangle ...

1 p 24 THEOREM . Let 1 sp < , and let Lp [ 0 , 1 ] be the space of all complex

valued , Borel - Lebesgue measurable functions defined in [ 0 , 1 ] and satisfying {

$ 15 ( 2 ) | P dx } " * = \ s \ < . Let g ( x , y ) be defined and

**continuous**on thetriangle ...

Page 2448

1 . + 1 THEOREM . Let X be a B - space , and let Te B ( X ) . Let A be an “ auxiliary

” B - space , with the norm | | | A | | | , A € A . Let M , and M , be real numbers

greater than zero . Suppose that : ( a ) a

, of ...

1 . + 1 THEOREM . Let X be a B - space , and let Te B ( X ) . Let A be an “ auxiliary

” B - space , with the norm | | | A | | | , A € A . Let M , and M , be real numbers

greater than zero . Suppose that : ( a ) a

**continuous**linear mapping q : A → B ( x ), of ...

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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