## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 90

Page 2169

To see that it is a homomorphism on the algebra of

To see that it is a homomorphism on the algebra of

**bounded**Borel functions , note that for a fixed continuous function g ... S M sup if ( 2 ) . λεσ ( Τ ) These facts show that the**operator**E ( o ) defined by ( iv ) is a**bounded**spectral ...Page 2239

Since f Xe is a bounded function , the operator T ' ( f Xe ) is a

Since f Xe is a bounded function , the operator T ' ( f Xe ) is a

**bounded operator**. If x is in E ( ē ) X as well as in E ( e ) X , it follows from the operational calculus for bounded functions ( cf. XVII.2.10 ) that T ( fXe ) x = T ...Page 2252

An attempt to follow the development in the

An attempt to follow the development in the

**bounded**case by writing N = T - S runs into difficulties . The**operator**N , although easily seen by Lemma 2 to have a quasi - nilpotent restriction to each space E ( o ) X with o**bounded**...### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 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 function 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