## 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

Since Â ( 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 Â ( 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

= A ( 04 ( : , u ( a ) ) ) ( cf . Lemma 4 for the definition of ula ) ) . Then , by the

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

we obtain the present corollary . Q . E . D . 5 COROLLARY . Under the

hypotheses of the

( 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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