## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 90

Page 2188

Let E be a spectral measure in the complex B - space X which is defined and

countably additive on a o - field of subsets of a

measurable function defined on the complex plane . Then $ 9 ( f ( n ) ) E ( da ) = g

...

Let E be a spectral measure in the complex B - space X which is defined and

countably additive on a o - field of subsets of a

**set**1 and let g be a bounded**Borel**measurable function defined on the complex plane . Then $ 9 ( f ( n ) ) E ( da ) = g

...

Page 2189

Hence for an arbitrary g in EB ( 1 , 2 ) , equation ( ii ) holds for every characteristic

function f of a set in E . But the set of f for which ( ii ) holds is ... Now E , is defined

and countably additive on the field of

Hence for an arbitrary g in EB ( 1 , 2 ) , equation ( ii ) holds for every characteristic

function f of a set in E . But the set of f for which ( ii ) holds is ... Now E , is defined

and countably additive on the field of

**Borel sets**and it commutes with S ( f ) .Page 2233

Let T be a spectral operator with resolution of the identity E , and let f be a

function analytic in an open set U such that E ( U ) ... The operator f ( T ) of

Definition 8 is closed , linear , and independent of the particular sequence of

Let T be a spectral operator with resolution of the identity E , and let f be a

function analytic in an open set U such that E ( U ) ... The operator f ( T ) of

Definition 8 is closed , linear , and independent of the particular sequence of

**Borel sets**used to ...### 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 | |

29 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 defined Definition denote dense determined differential operator discrete 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 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