## Linear Operators: Spectral theory |

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Page 1021

Nelson Dunford, Jacob T. Schwartz. preceding remarks that the final conclusion

of the lemma is equivalent to the

1 ( n - 1 ) - ( n - 1 ) / 2 . Now , since W is unitary , det ( A ) = det ( W - 1 AW ) and ( A

...

Nelson Dunford, Jacob T. Schwartz. preceding remarks that the final conclusion

of the lemma is equivalent to the

**statement**that | det ( A ) ( A - 1x , y ) = \ y \ || A || -1 ( n - 1 ) - ( n - 1 ) / 2 . Now , since W is unitary , det ( A ) = det ( W - 1 AW ) and ( A

...

Page 1756

( B ) The uniqueness of the function V of the theorem is an evident consequence

of

existence of the function V to the proof of the following

...

( B ) The uniqueness of the function V of the theorem is an evident consequence

of

**statement**( i ) . Moreover ,**statement**( 1 ) enables us to reduce the proof of theexistence of the function V to the proof of the following

**statement**. ( ii ) For each r...

Page 1771

... αε Σ , , and such that lim ( u ( t , . ) - 1 ( • ) ] = 0 . Proof .

from the preceding theorem and Theorem 6.23 .

hypotheses of ...

... αε Σ , , and such that lim ( u ( t , . ) - 1 ( • ) ] = 0 . Proof .

**Statement**( i ) followsfrom the preceding theorem and Theorem 6.23 .

**Statement**( ii ) follows from**statement**( ii ) of the preceding theorem , since a function satisfying thehypotheses of ...

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