## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

### From inside the book

Results 1-3 of 82

Page 2197

Let B be a complete ( o - complete ) Boolean algebra of projections in the B -

space X and let { Ex } be a monotone generalized

} is ...

Let B be a complete ( o - complete ) Boolean algebra of projections in the B -

space X and let { Ex } be a monotone generalized

**sequence**( a monotone**sequence**) in B. Then , if { Ex } is increasing , lim Enx = ( YE ) , X E X , while if { Ex} is ...

Page 2218

If a generalized

projections in a B - space converges weakly to a ... Let { Ex } be a weakly

convergent generalized

. It must ...

If a generalized

**sequence**of projections in a o - complete Boolean algebra ofprojections in a B - space converges weakly to a ... Let { Ex } be a weakly

convergent generalized

**sequence**in B and suppose that its limit E is a projection. It must ...

Page 2450

By Theorem X.3.4 there exists a complete orthonormal basis { Xn } consisting of

eigenvectors of T. We let Tan = in Un , 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 Tan = in Un , and suppose that none of the eigenvalues

in is multiple ( that is , that the

**sequence**{ n } contains no repetitions ) and that in...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 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 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