## 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 2400

Suppose that : ( a ) a continuous linear

, is given ; ( b ) a continuous linear

such that TI ( A ) – T ( A ) T = 9 ( A ) , A € A , is defined ; ( c ) a continuous bilinear

...

Suppose that : ( a ) a continuous linear

**mapping**q : A → B ( X ) of norm at most M, is given ; ( b ) a continuous linear

**mapping**T : A → B ( x ) , of norm at most M1 ,such that TI ( A ) – T ( A ) T = 9 ( A ) , A € A , is defined ; ( c ) a continuous bilinear

...

Page 2447

Let y be a monotone increasing function with two continuous derivatives ,

Let a ( x ) be a complex valued function with two continuous derivatives defined

in [ 0 , 1 ] .

Let y be a monotone increasing function with two continuous derivatives ,

**mapping**the interval [ 0 , 1 ] into itself . Let ☺ be the inverse of the**mapping**4 .Let a ( x ) be a complex valued function with two continuous derivatives defined

in [ 0 , 1 ] .

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 continuous linear

, 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