## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 76

Page 2209

This means that A = An ( A ) E ( A1 ) for sufficiently large integers n , from which it

clearly follows that A is in the

15 COROLLARY . The weakly closed operator algebra generated by a o ...

This means that A = An ( A ) E ( A1 ) for sufficiently large integers n , from which it

clearly follows that A is in the

**uniformly**closed algebra generated by B . Q . E . D .15 COROLLARY . The weakly closed operator algebra generated by a o ...

Page 2300

Then , since the collection of finite sums of projections E ( Nn ; T ) is

bounded , it is clear from [ * ] that the collection of finite sums of projections ElMn ;

T + P ) , n 2 K , is

...

Then , since the collection of finite sums of projections E ( Nn ; T ) is

**uniformly**bounded , it is clear from [ * ] that the collection of finite sums of projections ElMn ;

T + P ) , n 2 K , is

**uniformly**bounded . Moreover , Lan ( E ( An ; T ) – Elun ; T + P )...

Page 2361

Thus , as in the third paragraph of the proof of Theorem 6 , it is sufficient to show

that F * ( a ) = ( T + P ) * — 21 ) - 1f * is

* ) . However , in the course of the proof of Theorem 6 it was established that the ...

Thus , as in the third paragraph of the proof of Theorem 6 , it is sufficient to show

that F * ( a ) = ( T + P ) * — 21 ) - 1f * is

**uniformly**bounded for each fe So ( ( T + P )* ) . However , in the course of the proof of Theorem 6 it was established that the ...

### 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