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

### From inside the book

Results 1-3 of 79

Page 2108

143 ] used the word “ spectral ” ) if there

measure u on X to A and a bounded Baire measurable function f : X C such that a

= S f ( x ) p ( da ) . It follows that there

143 ] used the word “ spectral ” ) if there

**exists**a compact space X , a spectralmeasure u on X to A and a bounded Baire measurable function f : X C such that a

= S f ( x ) p ( da ) . It follows that there

**exists**a spectral measure va defined on a ...Page 2278

There

for each F * € 8 * , m ( F * ) is the least cardinal power of a set of cyclic subspaces

spanning F *** in the X - topology . There is a unique decomposition of the ...

There

**exists**a unique multiplicity function m defined on B * with the property thatfor each F * € 8 * , m ( F * ) is the least cardinal power of a set of cyclic subspaces

spanning F *** in the X - topology . There is a unique decomposition of the ...

Page 2405

If he L , ( s , E , p ) and 2 Sr < oo , it follows that the integral ( 14 ) ( Ah ) ( s ) = ; 14 (

8,4 ) | h ( ) u ( dt )

element f of L. ( S , E , j ) , we have | Ah , $ { A } , | h \ ,. Thus , using Theorem ...

If he L , ( s , E , p ) and 2 Sr < oo , it follows that the integral ( 14 ) ( Ah ) ( s ) = ; 14 (

8,4 ) | h ( ) u ( dt )

**exists**for u - almost all s , and that , writing ifle for the norm of anelement f of L. ( S , E , j ) , we have | Ah , $ { A } , | h \ ,. Thus , using Theorem ...

### 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