## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 85

Page 2160

It will next be

) X . To see this it will , in view of Corollary II . 3 . 13 , suffice to show that x * ( x - y

) = 0 for every linear functional x * which vanishes on ( 101 – T ) X . If xc * is ...

It will next be

**shown**that the vector x - y is in the closure of the manifold ( 1 . 1 – T) X . To see this it will , in view of Corollary II . 3 . 13 , suffice to show that x * ( x - y

) = 0 for every linear functional x * which vanishes on ( 101 – T ) X . If xc * is ...

Page 2246

It may be

positive integers , and Hj = Enes Hin ) , then the spectrum of the restriction C | H ,

is J . Since ( iI – C ) - 1 is bounded , il – C is closed . Thus C is closed . Let Pin ...

It may be

**shown**in precisely the same way that if J is a subset of the class ofpositive integers , and Hj = Enes Hin ) , then the spectrum of the restriction C | H ,

is J . Since ( iI – C ) - 1 is bounded , il – C is closed . Thus C is closed . Let Pin ...

Page 2266

It will be

multiplicity on B , Lemma 2 permits us to restrict our attention to C . 5 LEMMA .

The set 6 is a dense o - ideal in B . A projection belongs to C if and only if it is the

carrier ...

It will be

**shown**that C is a dense o - ideal in B and thus , in defining themultiplicity on B , Lemma 2 permits us to restrict our attention to C . 5 LEMMA .

The set 6 is a dense o - ideal in B . A projection belongs to C if and only if it is the

carrier ...

### 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

algebra of projections analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear closure commuting compact complete consider constant contained 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 positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero