## 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 2011

For every set o in and every such matrix Â ( s ) we

For every set o in and every such matrix Â ( s ) we

**define**the matrix ( 1 ) 4 ( 8 ) = 4 ( s ) , SEO , = 0 , 80 , and the operator Â , in Ho ... It is clear that for such sets o the operator Âo is a bounded everywhere**defined**operator .Page 2018

in the notation for the natural closed extension As , for in this case the symbol A is used for the restriction As to , that is , the formal differential operator which

in the notation for the natural closed extension As , for in this case the symbol A is used for the restriction As to , that is , the formal differential operator which

**defines**As . The spectra of the unbounded operators we have been ...Page 2284

It follows from Lemma 18 and Theorem 19 that there exist vectors x1 , ... , Xn and functions 2 * , mention such that EnX = VT - 1 M ( xx ) , x * ( V 1 + 1 M ( xx ) ) = 0 , and the measures = x ; = My = x * E ( : ) xt , now

It follows from Lemma 18 and Theorem 19 that there exist vectors x1 , ... , Xn and functions 2 * , mention such that EnX = VT - 1 M ( xx ) , x * ( V 1 + 1 M ( xx ) ) = 0 , and the measures = x ; = My = x * E ( : ) xt , now

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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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### 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 defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension 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