## Linear Operators: Spectral operators |

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Page 2130

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. K = { x €

V10 < x } is called the

K satisfies ( i ) K + K SK , ( ii ) K & K for all de R , 120 , and ( iii ) Kn ( - K ) = { 0 } .

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. K = { x €

V10 < x } is called the

**positive**cone of V ( with respect to S ) ; it is easy to see thatK satisfies ( i ) K + K SK , ( ii ) K & K for all de R , 120 , and ( iii ) Kn ( - K ) = { 0 } .

Page 2461

3 , R is the unique

operator V * V . As is observed in the first sentence of Section XI . 9 , ( V * V ) 1 / 2

is compact . Lemma 10 now follows immediately from Definition XI . 9 . 1 .

3 , R is the unique

**positive**square root ( V * V ) 1 / 2 of the bounded self adjointoperator V * V . As is observed in the first sentence of Section XI . 9 , ( V * V ) 1 / 2

is compact . Lemma 10 now follows immediately from Definition XI . 9 . 1 .

Page 2564

2 . A remark on the Volterra operator . J . Math . Anal . Appl . 12 , 244 – 246 (

1965 ) . 3 . Invariant subspaces and unstarred operator algebras . Pacific J . Math

. 17 , 511 - 517 ( 1966 ) . Sasser , D . W . 1 . Quasi -

2 . A remark on the Volterra operator . J . Math . Anal . Appl . 12 , 244 – 246 (

1965 ) . 3 . Invariant subspaces and unstarred operator algebras . Pacific J . Math

. 17 , 511 - 517 ( 1966 ) . Sasser , D . W . 1 . Quasi -

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