## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 92

Page 2197

Let B be a complete ( o - complete ) Boolean algebra of projections in the B - space X and let { Ea } be a monotone generalized

Let B be a complete ( o - complete ) Boolean algebra of projections in the B - space X and let { Ea } be a monotone generalized

**sequence**( a monotone**sequence**) in B. Then , if { Ex } is increasing , lim EX ( V Ed ) , Eg X e X , while ...Page 2218

Let { Ex } be a weakly convergent generalized

Let { Ex } be a weakly convergent generalized

**sequence**in B and suppose that its limit E is a projection . It must be shown that { Ea } converges strongly to E. By Lemma 6 , E is in B and so a consideration of the**sequence**{ E ...Page 2450

By Theorem X.3.4 there exists a complete orthonormal basis { xn } consisting of eigenvectors of T. We let Txn = nXn , and suppose that none of the eigenvalues in is multiple ( that is , that the

By Theorem X.3.4 there exists a complete orthonormal basis { xn } consisting of eigenvectors of T. We let Txn = nXn , and suppose that none of the eigenvalues in is multiple ( that is , that the

**sequence**{ n } contains no repetitions ) ...### 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 | 1931 |

Copyright | |

30 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 domain elements equation equivalent established exists extension 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