## 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 84

Page 1955

We shall be concerned with the fine structure of the

points of an operator in X will be classified , as they were in Hilbert space ,

according to the following definition . + 1 DEFINITION . Let A be a bounded linear

...

We shall be concerned with the fine structure of the

**spectrum**, and the spectralpoints of an operator in X will be classified , as they were in Hilbert space ,

according to the following definition . + 1 DEFINITION . Let A be a bounded linear

...

Page 1957

Thus , by the preceding corollary , we have O ( S . ) Soc ( To ) , and so to prove

the present corollary , it suffices to prove that , is in the continuous

. Let ( S – XI ) x = 0 , where x is in E ( 0 ) X . Since S and T have the same ...

Thus , by the preceding corollary , we have O ( S . ) Soc ( To ) , and so to prove

the present corollary , it suffices to prove that , is in the continuous

**spectrum**of Sg. Let ( S – XI ) x = 0 , where x is in E ( 0 ) X . Since S and T have the same ...

Page 2507

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

Theodore Schwartz. uniformly bounded by a constant K in the neighborhood of

the

...

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

Theodore Schwartz. uniformly bounded by a constant K in the neighborhood of

the

**spectrum**of H , while the integrals ( ( 1 + i€ ) 1 – H ) – 15 / 2 dx and + 8 8 + 8 1...

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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