## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 89

Page 2188

Let f be in EB ( 1 , 2 ) , and for every

Let f be in EB ( 1 , 2 ) , and for every

**Borel set**8 in the complex plane let E ( 8 ) = E ( f - ( 8 ) ) . If g is the characteristic function of such a set ...Page 2189

Now Ey is defined and countably additive on the field of

Now Ey is defined and countably additive on the field of

**Borel sets**and it commutes with S ( f ) . Thus to see that E1 is the resolution of the identity for ...Page 2233

The operator f ( T ) of Definition 8 is closed , linear , and independent of the particular sequence of

The operator f ( T ) of Definition 8 is closed , linear , and independent of the particular sequence of

**Borel sets**used to define it . ( i ) For each Borel ...### 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