## 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 2147

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. resolution of the identity for T ... Conversely , let the bounded

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. resolution of the identity for T ... Conversely , let the bounded

**linear operator**T satisfy conditions ( A ) , ( B ) , and ( C ) . Then , by Theorem 3 .Page 2162

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. PROOF . If the bounded

complete space has properties ( B ) and ( G ) then , by Lemma 4 , it has

properties ( A ) ...

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. PROOF . If the bounded

**linear operator**T in a weaklycomplete space has properties ( B ) and ( G ) then , by Lemma 4 , it has

properties ( A ) ...

Page 2400

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. 2 . ... Let X be a B - space , and let T be a

; let K be a second

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. 2 . ... Let X be a B - space , and let T be a

**linear operator**in X; let K be a second

**linear operator**in X which is , in a sense to be made precise ...### What people are saying - Write a review

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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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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