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

### From inside the book

Results 1-3 of 26

Page 2118

A generalized scalar operator Te B ( X ) is said to be

spectral distribution . Although it is not known whether or not every generalized

scalar operator is

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 generalized

scalar operator is

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

Page 2158

If the set of points

subinterval of To whose end points are

Borel subset of the plane is measurable T . PROOF . Let y be a closed subinterval

of To ...

If the set of points

**regular**relative to T is dense on To , then every closedsubinterval of To whose end points are

**regular**relative to T is in S ( T ) and everyBorel subset of the plane is measurable T . PROOF . Let y be a closed subinterval

of To ...

Page 2160

1 - T ) X . Since do is interior to an interval of constancy relative to T , it is

therefore a

and if the adjoint T * satisfies the boundedness condition ( B ) , then the

points ...

1 - T ) X . Since do is interior to an interval of constancy relative to T , it is

therefore a

**regular**point relative to T . Q . E . D . 14 LEMMA ( G ) . If X is reflexiveand if the adjoint T * satisfies the boundedness condition ( B ) , then the

**regular**points ...

### 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