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

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Page 2209

This means that A = An = 5 ( A ) E ( A1 ) for sufficiently large integers n , from

which it clearly follows that A is in the

Q . E . D . 15 COROLLARY . The weakly closed operator algebra generated by

a o ...

This means that A = An = 5 ( 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 2361

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

that F * ( a ) = ( ( T + P ) * — XI ) - 18 * is

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

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

that F * ( a ) = ( ( T + P ) * — XI ) - 18 * is

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

Page 2382

We shall now show that the second expression on the right of ( 14 ) converges to

zero as lu ] 00 , u remaining in P + ,

sequence of functions in Co [ 0 , 0 ) , each vanishing outside a bounded subset of

[ 0 , 0 ) ...

We shall now show that the second expression on the right of ( 14 ) converges to

zero as lu ] 00 , u remaining in P + ,

**uniformly**for 0 < t < o . Let { an } be asequence of functions in Co [ 0 , 0 ) , each vanishing outside a bounded subset of

[ 0 , 0 ) ...

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