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

### From inside the book

Results 1-3 of 95

Page 2094

12 ) that if X is a weakly complete B - space , then any prespectral

automatically

and Dowson [ 1 ] have considered prespectral

...

12 ) that if X is a weakly complete B - space , then any prespectral

**operator**isautomatically

**spectral**, and so has a unique resolution of the identity . Berksonand Dowson [ 1 ] have considered prespectral

**operators**in some detail and have...

Page 2118

A generalized scalar

scalar

two ...

A generalized scalar

**operator**Te B ( X ) is said to be regular if it has a regular**spectral**distribution . Although it is not known whether or not every generalizedscalar

**operator**is regular ( unless the**spectrum**is sufficiently " thin " ) , given anytwo ...

Page 2590

Restriction of a

mechanical three - body problem , XX . 6 ( 2501 ) , ( 2507 ) Quantum theory of

fields , XX . 6 ( 2501 ) , ( 2507 ) Quasi - nilpotent operator , definition of , XV . 4 . 2

( 1938 ) ...

Restriction of a

**spectral operator**, spectrum of , XV . 8 . 5 ( 1956 ) Quantummechanical three - body problem , XX . 6 ( 2501 ) , ( 2507 ) Quantum theory of

fields , XX . 6 ( 2501 ) , ( 2507 ) Quasi - nilpotent operator , definition of , XV . 4 . 2

( 1938 ) ...

### What people are saying - Write a review

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

### Other editions - View all

### Common terms and phrases

adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero