## 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 1955

We shall be concerned with the fine structure of the

We shall be concerned with the fine structure of the

**spectrum**, and the spectral points of an operator in X will be classified , as they were in Hilbert space , according to the following definition . + 1 DEFINITION .Page 2507

uniformly bounded by a constant K in the neighborhood of the

uniformly bounded by a constant K in the neighborhood of the

**spectrum**of H , while the integrals S ** 4 ( ( A + ie ) I – H ) - 10l2 dx and S * * B * ( ( A + ie ) 1 – H ) 10l2 da are bounded as ĉ → 0 . In this case , and under the ...Page 2591

... XV.2 ( 1930 )

... XV.2 ( 1930 )

**Spectrum**, of a spectral operator , XV.8 ( 1954 ) condition to be in point**spectrum**, XV.15.13 ( 2076 ) continuous**spectrum**, definition of , XV.8.1 ( 1955 ) examples of , XV.15.37 , XV.15.38 , XV.15.39 ( 2080 ) point ...### 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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### 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