## 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 XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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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