## 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 2094

12 ) that if X is a weakly complete B - space , then any prespectral operator is

automatically spectral , and so has a

and Dowson [ 1 ] have considered prespectral operators in some detail and have

...

12 ) that if X is a weakly complete B - space , then any prespectral operator is

automatically spectral , and so has a

**unique**resolution of the identity . Berksonand Dowson [ 1 ] have considered prespectral operators in some detail and have

...

Page 2143

Let T be a bounded linear operator in the complex B - space X . Then there is a

( T ) , g ( x ) Ş8 , de S ( T ) , ( 2 ) 58 ' . This spectral measure is bounded , is ...

Let T be a bounded linear operator in the complex B - space X . Then there is a

**unique**spectral measure on the field S ( T ) with the properties E ( S ) x = x , de S( T ) , g ( x ) Ş8 , de S ( T ) , ( 2 ) 58 ' . This spectral measure is bounded , is ...

Page 2265

Let D be a dense ideal in B and m be a function on D to cardinals such that m ( 0

) = 0 and m ( Va E . ) = Vam ( Ed ) for each family { E } = D for which V . Ece D .

Then there is a

Let D be a dense ideal in B and m be a function on D to cardinals such that m ( 0

) = 0 and m ( Va E . ) = Vam ( Ed ) for each family { E } = D for which V . Ece D .

Then there is a

**unique**multiplicity function on B which is an extension of m on D ...### What people are saying - Write a review

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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