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

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Page 2098

The following

Smart [ 2 ] . Let Te B ( x ) with o ( T ) = 0 . ( T ) = [ 0 , 1 ] with a bounded commuting

strongly continuous family E ( t ) , te [ 0 , 1 ] , of projections such that ( i ) E ( 0 ) ...

The following

**result**was proved by Sine [ 1 ] , using techniques similar to those inSmart [ 2 ] . Let Te B ( x ) with o ( T ) = 0 . ( T ) = [ 0 , 1 ] with a bounded commuting

strongly continuous family E ( t ) , te [ 0 , 1 ] , of projections such that ( i ) E ( 0 ) ...

Page 2214

Q . E . D . The preceding material of the present section was largely preliminary to

the following basic

THEOREM . Let B be a bounded Boolean algebra of projections in a weakly ...

Q . E . D . The preceding material of the present section was largely preliminary to

the following basic

**result**of Bade , which was described in the introduction . 18THEOREM . Let B be a bounded Boolean algebra of projections in a weakly ...

Page 2348

Then the present

Theorem 8 , Theorem 13 , and Lemma 15 once we showed that ( using the

notations of the hypothesis of Theorem 2 . 7 ) = 1 dona ( 11 . m . + dm ) 2 ( n − 2 )

/ n < 0o .

Then the present

**result**would follow from Theorem 2 . 7 , Corollary 2 . 8 ,Theorem 8 , Theorem 13 , and Lemma 15 once we showed that ( using the

notations of the hypothesis of Theorem 2 . 7 ) = 1 dona ( 11 . m . + dm ) 2 ( n − 2 )

/ n < 0o .

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