## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 84

Page 1913

... x in the complex B - space in which T operates , the analytic function R ( a ; T ) x has only single valued extensions . ... and are usually set in

... x in the complex B - space in which T operates , the analytic function R ( a ; T ) x has only single valued extensions . ... and are usually set in

**Hilbert space**, since the presentation is shorter than that for other B - spaces .Page 1945

Bounded Spectral Operators in

Bounded Spectral Operators in

**Hilbert Space**What is the relationship between the bounded spectral operators in a**Hilbert space**H and the bounded normal operators in H ? The central result in this direction is a theorem of Wermer which ...Page 1963

Since HP is a

Since HP is a

**Hilbert space**, there is ( IV.4.5 ) a uniquely defined point y = [ 41 , ... , yp ] in HP such that x * x = ( x , y ) for every x in Ho , and this unique y also has the property that ( x * = \ y .### 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