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

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Page 1979

It follows from equations ( iv ) and ( v ) of Lemma 3 that Eld ( s ) ; Â ( s ) ) is e -

essentially bounded on S . Lemma 4 then

is satisfied . Q . E . D . 8 COROLLARY . Every operator A in AP is the strong limit

of ...

It follows from equations ( iv ) and ( v ) of Lemma 3 that Eld ( s ) ; Â ( s ) ) is e -

essentially bounded on S . Lemma 4 then

**shows**that condition ( i ) of the theoremis satisfied . Q . E . D . 8 COROLLARY . Every operator A in AP is the strong limit

of ...

Page 2169

This

continuous function g . A repetition of this argument

and g are both bounded Borel functions . Thus the operators f ( T ) and g ( T )

commute and ...

This

**shows**that ( vi ) holds for every bounded Borel function f and everycontinuous function g . A repetition of this argument

**shows**that it also holds if fand g are both bounded Borel functions . Thus the operators f ( T ) and g ( T )

commute and ...

Page 2170

These lemmas will

... If a is not real , an expansion of the scalar product ( ( QI – T ) x , ( aI – T ) x )

...

These lemmas will

**show**that the hypotheses of Theorem 5 . 18 are satisfied by a... If a is not real , an expansion of the scalar product ( ( QI – T ) x , ( aI – T ) x )

**shows**that llal — T ' ) l2 = | | ( a ) a [ 2 + | ( R ( Q ) I – T ) « [ ? 2 | I ( 0 ) | 2 [ 2 / 2 , so...

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