## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 94

Page 2209

... follows that A is in the uniformly

COROLLARY . The weakly

Boolean algebra B which satisfies the condition of the preceding lemma is the

same ...

... follows that A is in the uniformly

**closed**algebra generated by B. Q.E.D. 15COROLLARY . The weakly

**closed**operator algebra generated by a o - completeBoolean algebra B which satisfies the condition of the preceding lemma is the

same ...

Page 2214

By Corollary VI.1.5 , the weakly

the same as the strongly

is the strong limit of finite linear combinations of elements of B. It follows that A ...

By Corollary VI.1.5 , the weakly

**closed**operator algebra W ( B ) generated by B isthe same as the strongly

**closed**algebra generated by B. Thus every A in W ( B )is the strong limit of finite linear combinations of elements of B. It follows that A ...

Page 2217

A bounded linear operator is in the weakly

a o - complete Boolean algebra B of projections in a B - space if and only if it

leaves invariant every

every ...

A bounded linear operator is in the weakly

**closed**operator algebra generated bya o - complete Boolean algebra B of projections in a B - space if and only if it

leaves invariant every

**closed**linear manifold which remains invariant underevery ...

### 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