## 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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Results 1-3 of 79

Page 1947

Let B1 , . . . , Bk be a finite collection of commuting bounded Boolean algebras of

projections in a Hilbert space H . Then there exists a bounded self

a self ...

Let B1 , . . . , Bk be a finite collection of commuting bounded Boolean algebras of

projections in a Hilbert space H . Then there exists a bounded self

**adjoint****operator**B in H with a bounded everywhere defined inverse such that BEB - 1 isa self ...

Page 2170

18 are satisfied by a self

bounded self

non - real a we have | R ( Q ; T ) 3 , PROOF . If a is not real , an expansion of the ...

18 are satisfied by a self

**adjoint operator**in Hilbert space . 1 LEMMA . If T is abounded self

**adjoint operator**in Hilbert space , its spectrum is real and for everynon - real a we have | R ( Q ; T ) 3 , PROOF . If a is not real , an expansion of the ...

Page 2478

Let H4 be a self

identity E4 ( : ) . Suppose that V4 is a symmetric operator in H , that D ( VA ) 2 D (

H4 ) , that the operator V ( il – H2 ) - 1 is compact , and that for each bounded ...

Let H4 be a self

**adjoint operator**in H , with domain D ( H , ) and resolution of theidentity E4 ( : ) . Suppose that V4 is a symmetric operator in H , that D ( VA ) 2 D (

H4 ) , that the operator V ( il – H2 ) - 1 is compact , and that for each bounded ...

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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