Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |
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Results 1-3 of 91
Page 1983
The argument of the preceding corollary shows that A is a spectral operator .
Since  ( s ) has distinct eigenvalues , it is a scalar operator , that is , its radical
part is zero . Thus Corollary 9 shows that A is also a scalar type operator . Q . E .
D . 11 ...
The argument of the preceding corollary shows that A is a spectral operator .
Since  ( s ) has distinct eigenvalues , it is a scalar operator , that is , its radical
part is zero . Thus Corollary 9 shows that A is also a scalar type operator . Q . E .
D . 11 ...
Page 2396
Let o4 be as in the preceding lemma , put A ( N ) = A ( Qili , ul2 ) ) ) , and let B ( A )
= A ( 04 ( : , u ( a ) ) ) ( cf . Lemma 4 for the definition of ula ) ) . Then , by the
preceding lemma , by Lemma 1 , and by formulas ( 2a ) and ( 2b ) , ( B ( A ) ] ~ A (
2 ) ...
Let o4 be as in the preceding lemma , put A ( N ) = A ( Qili , ul2 ) ) ) , and let B ( A )
= A ( 04 ( : , u ( a ) ) ) ( cf . Lemma 4 for the definition of ula ) ) . Then , by the
preceding lemma , by Lemma 1 , and by formulas ( 2a ) and ( 2b ) , ( B ( A ) ] ~ A (
2 ) ...
Page 2455
Therefore , if we let the three operators of the preceding lemma be H2 , H1 , H1 ,
we obtain the present corollary . Q . E . D . 5 COROLLARY . Under the
hypotheses of the preceding corollary , U ( H1 , H2 ) is an isometric mapping of E
( H1 , H2 ) ...
Therefore , if we let the three operators of the preceding lemma be H2 , H1 , H1 ,
we obtain the present corollary . Q . E . D . 5 COROLLARY . Under the
hypotheses of the preceding corollary , U ( H1 , H2 ) is an isometric mapping of E
( H1 , H2 ) ...
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