## 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 |

### From inside the book

Results 1-3 of 92

Page 2107

been studied in connection with ( partially ) ordered spaces by Schaefer [ 7 , 10 ,

11 ] , Schaefer and Walsh [ 1 ] , and Walsh [ 1 , 2 , 3 ] . We shall give a condensed

...

**Spectral measures**, locally convex spaces and order .**Spectral measures**havebeen studied in connection with ( partially ) ordered spaces by Schaefer [ 7 , 10 ,

11 ] , Schaefer and Walsh [ 1 ] , and Walsh [ 1 , 2 , 3 ] . We shall give a condensed

...

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Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the

Assistance of William G. Bade and ... One of the most surprising results due to

Walsh [ 2 ] is the result that if u is an equicontinuous Borel

the ...

Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the

Assistance of William G. Bade and ... One of the most surprising results due to

Walsh [ 2 ] is the result that if u is an equicontinuous Borel

**spectral measure**intothe ...

Page 2591

definition of, XVI.4.1 (2145) Spectral operators, in 91'', condition for, XV. ... spaces

, XVII.5.16 (2225) Subscalar operators, XV.16 (2095-2096) Support, of a

definition of, XVI.4.1 (2145) Spectral operators, in 91'', condition for, XV. ... spaces

, XVII.5.16 (2225) Subscalar operators, XV.16 (2095-2096) Support, of a

**spectral****measure**, XV.9 (1965) Tempered distribution in RN, complex conjugate of, XV.### What people are saying - Write a review

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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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### Common terms and phrases

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