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

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Page 2082

Show that Ø and Y are bounded linear operators and that D ( F ) ¥ ( h ) = f f ( s ) h

( 8 ) 4 ( 8 ) x * E ( ds ) xo S 50 ( McCarthy ) Continuing the preceding

XY , Xo , and 0 . be chosen so that x * E ( 0 . ) X . # 0 and let g be the Radon ...

Show that Ø and Y are bounded linear operators and that D ( F ) ¥ ( h ) = f f ( s ) h

( 8 ) 4 ( 8 ) x * E ( ds ) xo S 50 ( McCarthy ) Continuing the preceding

**exercise**, letXY , Xo , and 0 . be chosen so that x * E ( 0 . ) X . # 0 and let g be the Radon ...

Page 2172

8 ( Fixman ) Let T be as in the preceding

Banach limit as in

63 , . . . ) = ( g ( x ) , 0 , 0 , . . . ) . Show that A2 = 0 and that o ( TX ) = P ( x ) and AT

= TA .

8 ( Fixman ) Let T be as in the preceding

**exercise**and let y in ( 1 . 0 ) * be aBanach limit as in

**Exercise**II . 4 . 22 . Let A be defined on lo by Ax = A ( 61 , 62 ,63 , . . . ) = ( g ( x ) , 0 , 0 , . . . ) . Show that A2 = 0 and that o ( TX ) = P ( x ) and AT

= TA .

Page 2489

exist operators A , B of the Hilbert - Schmidt class , depending only on V and H ,

such that ( W . – U , rl2 = ( S . 4 exp ( – ixH ) vol dx ) 1 / 2 1 / 2 x { f } B exp –

iektyolje ...

**Exercise**17 . ) ( a ) Show that the limit W w = lim + . U . W exists , and that thereexist operators A , B of the Hilbert - Schmidt class , depending only on V and H ,

such that ( W . – U , rl2 = ( S . 4 exp ( – ixH ) vol dx ) 1 / 2 1 / 2 x { f } B exp –

iektyolje ...

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