## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 88

Page 2299

Hence we find that for n

( y ; T + P ) = B ( u ) . Since Blu ) is clearly the product of the compact operator R (

u ; T ) and a bounded operator , it follows that T + P is a discrete operator .

Hence we find that for n

**sufficiently**large , each u in Cn is in p ( T + P ) and that R( y ; T + P ) = B ( u ) . Since Blu ) is clearly the product of the compact operator R (

u ; T ) and a bounded operator , it follows that T + P is a discrete operator .

Page 2300

Since E , + Xiai Elan ; T ) = 1 , 1 - Ê has a finite dimensional range for all p . Thus ,

by Lemma VII . 6 . 7 , I - E , has finite dimensional range for all

Since E is a countably additive spectral resolution , we have Elu ; T + P ) ( I – E ...

Since E , + Xiai Elan ; T ) = 1 , 1 - Ê has a finite dimensional range for all p . Thus ,

by Lemma VII . 6 . 7 , I - E , has finite dimensional range for all

**sufficiently**large p .Since E is a countably additive spectral resolution , we have Elu ; T + P ) ( I – E ...

Page 2394

Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution og ( t ,

) of the equation to = u o , defined for 0 St < oo and for all

, such that og and os are continuous in t and u for 0 St < oo and pe

Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution og ( t ,

) of the equation to = u o , defined for 0 St < oo and for all

**sufficiently**small u € P +, such that og and os are continuous in t and u for 0 St < oo and pe

**sufficiently**...### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

### Other editions - View all

### Common terms and phrases

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