## 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 87

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 ) Şo ( To ) , and so to prove the

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

( S – 11 ) x = 0 , where x is in E ( 0 ) X . Since S and T have the same resolution ...

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

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

**spectrum**of S . . Let( S – 11 ) x = 0 , where x is in E ( 0 ) X . Since S and T have the same resolution ...

Page 2591

2 (1930) Spectral set for an operator, XV.2 (1930)

operator, XV.8 (1954) condition to be in point

continuous

15.38, XV. 15.

2 (1930) Spectral set for an operator, XV.2 (1930)

**Spectrum**, of a spectraloperator, 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.

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero