## 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

It follows from some results of Bade [ 4 ] ( see also XVII.2.1 and XVII.2.12 ) that if X is a weakly complete B - space , then any prespectral operator is automatically spectral , and so has a

It follows from some results of Bade [ 4 ] ( see also XVII.2.1 and XVII.2.12 ) 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 .Page 2143

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

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 ( 8 ) = x , = = 0 , de S ( T ) , g ( x ) = 8 , de S ( T ) , g ( x ) = 8 ' .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. ) = Væm ( Ec ) for each family { Ex } $ D for which VaEge 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. ) = Væm ( Ec ) for each family { Ex } $ D for which VaEge D. Then there is a

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

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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