## 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 67

Page 2285

Moreover if P ,

Moreover if P ,

**denotes**the perpendicular projection of H onto Hn , then D ( A - 1 ) = { h | Pnhe D ( , ) for all n and į ... in X. Let B**denote**the range of the resolution of the identity E ( • ) of Q XVIII.3.35 2285 MULTIPLICITY THEORY.Page 2286

For each bounded Borel function g on the plane let Š ( g )

For each bounded Borel function g on the plane let Š ( g )

**denote**the closure of AS ( g ) A - 1 . The correspondence : S ( g ) + Š ( 9 ) preserves the operational calculus and Q = Sc XẾ ( da ) , O ( Q ) where 7E ( e ) = E ( e ) , e € B.Page 2436

Next , let C. ( En )

Next , let C. ( En )

**denote**the set of all infinitely often differentiable complex valued functions defined in En and vanishing outside a bounded set , let g e Co ( En ) , and let g = f , with f € L2 ( En ) , so that , by the Plancherel ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 other sections not shown

### Other editions - View all

### 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