## 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 1945

Spectral Theory : Self Adjoint Operators in

Theodore Schwartz. is in the radical of the closed commutative subalgebra of B (

X ) generated by I , S , and N . Lemma IX . 1 . 12 ( e ) shows that this radical is ...

Spectral Theory : Self Adjoint Operators in

**Hilbert Space**Nelson Dunford, JacobTheodore Schwartz. is in the radical of the closed commutative subalgebra of B (

X ) generated by I , S , and N . Lemma IX . 1 . 12 ( e ) shows that this radical is ...

Page 2169

Spectral Theory : Self Adjoint Operators in

Theodore Schwartz. uniform limit of analytic functions , it follows that this map is

also a homomorphism on the algebra of continuous functions . To see that it is a ...

Spectral Theory : Self Adjoint Operators in

**Hilbert Space**Nelson Dunford, JacobTheodore Schwartz. uniform limit of analytic functions , it follows that this map is

also a homomorphism on the algebra of continuous functions . To see that it is a ...

Page 2528

Spectral Theory : Self Adjoint Operators in

Theodore Schwartz. 5 . Boolean algebras of projections of finite multiplicity .

Pacific J . Math . 9 , 681693 ( 1959 ) . 6 . Finite dimensional perturbations in

Banach ...

Spectral Theory : Self Adjoint Operators in

**Hilbert Space**Nelson Dunford, JacobTheodore Schwartz. 5 . Boolean algebras of projections of finite multiplicity .

Pacific J . Math . 9 , 681693 ( 1959 ) . 6 . Finite dimensional perturbations in

Banach ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 other sections not shown

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### Common terms and phrases

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 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