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

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Page 1953

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. 11 COROLLARY . If E ( { 0 } ) = 0 , then the operator A = 0 is

the only bounded linear operator for which either AT = 0 or TA = 0 .

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. 11 COROLLARY . If E ( { 0 } ) = 0 , then the operator A = 0 is

the only bounded linear operator for which either AT = 0 or TA = 0 .

**PROOF**.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 « , 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 « , ß are complex numbers and x , y are

vectors in ...

Page 2192

This shows that o ( $ ( J ) ) 25 ( 0 ) 2 n 1 ( 8 ) and completes the

lemma , Q . E . D . 12 COROLLARY . Let A be an algebra of operators in a weakly

complete B - space X . Suppose that A is topologically and algebraically

isomorphic ...

This shows that o ( $ ( J ) ) 25 ( 0 ) 2 n 1 ( 8 ) and completes the

**proof**of thelemma , Q . E . D . 12 COROLLARY . Let A be an algebra of operators in a weakly

complete B - space X . Suppose that A is topologically and algebraically

isomorphic ...

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