## Linear Operators: Spectral operators |

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Page 2137

Even though ( A ) is taken as a standing assumption throughout this section , it

will be indicated parenthetically in the statement of each lemma in the

which it is used . 1 LEMMA ( A ) . If a , ß are complex numbers and x , y are

vectors in ...

Even though ( A ) is taken as a standing assumption throughout this section , it

will be indicated parenthetically in the statement of each lemma in the

**proof**ofwhich it is used . 1 LEMMA ( A ) . If a , ß are complex numbers and x , y are

vectors in ...

Page 2232

1 + 00 To complete the

( Q ) , then limnt . Elên ) x = x and by the argument of the second paragraph of the

present

1 + 00 To complete the

**proof**of the theorem it will be shown that Q = Q . If x is in D( Q ) , then limnt . Elên ) x = x and by the argument of the second paragraph of the

present

**proof**, | Ca = lim do EVẽ ) = lim QE ( ẽ ) . no n + 00 Since Q is closed ...Page 2396

Then , by equations ( 22 ) and ( 23 ) of that same

ds ) " + \ | - - 2668 – q ( s ) dsl . It follows from this formula just as in the

Lemma 1 ( cf . the paragraph following formula ( 14 ) ) that lim fu ( t ) = 0 ,

uniformly ...

Then , by equations ( 22 ) and ( 23 ) of that same

**proof**, \ 320 ) 514 - { . $ 1906 ) |ds ) " + \ | - - 2668 – q ( s ) dsl . It follows from this formula just as in the

**proof**ofLemma 1 ( cf . the paragraph following formula ( 14 ) ) that lim fu ( t ) = 0 ,

uniformly ...

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