## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 86

Page 1977

The

by equation ( ii ) is a countably additive spectral measure in HP defined on the

Borel sets B in the complex plane . Since E ( 0 ; Â ( s ) ) and Â ( s ) commute for ...

The

**preceding**theorem shows that the operator valued measure E ( o ; A ) givenby equation ( ii ) is a countably additive spectral measure in HP defined on the

Borel sets B in the complex plane . Since E ( 0 ; Â ( s ) ) and Â ( s ) commute for ...

Page 2232

Let { en } be as in the

E ( en ) xc = E ( e ) x , and lim QE ( en ) E ( e ) x = lim QE ( ene ) x n + 00 n + 00 =

lim E ( ene ) Qx = E ( e ) Qx n 00 by the second paragraph of the

Let { en } be as in the

**preceding**proof , and let x be in D ( Q ) . Then limn + . E ( e )E ( en ) xc = E ( e ) x , and lim QE ( en ) E ( e ) x = lim QE ( ene ) x n + 00 n + 00 =

lim E ( ene ) Qx = E ( e ) Qx n 00 by the second paragraph of the

**preceding**...Page 2396

Let 04 be as in the

) = A ( 04 ( : , ula ) ) ) ( cf . Lemma 4 for the definition of ula ) ) . Then , by the

as ...

Let 04 be as in the

**preceding**lemma , put A ( a ) = A ( 01 ( : , u ( ) ) ) , and let B ( a) = A ( 04 ( : , ula ) ) ) ( cf . Lemma 4 for the definition of ula ) ) . Then , by the

**preceding**lemma , by Lemma 1 , and by formulas ( 2a ) and ( 2b ) , ( B ( ) ~ | A ) |as ...

### 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