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

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Page 2154

( G ) The spectrum

there is an integer valued function v defined on lo such that for every do in lo , la -

do ) " ( 10 ) R ( ;

( G ) The spectrum

**of T**is contained in the rectifiable Jordan curve 1o . Moreover ,there is an integer valued function v defined on lo such that for every do in lo , la -

do ) " ( 10 ) R ( ;

**T**) / 31 , # do , de 420In the analysis to follow , it is this ...Page 2159

9 every subset of p (

since o (

of Lemma 10 , it behooves us to seek conditions under which the points on I ,

which ...

9 every subset of p (

**T**) is in S (**T**) and hence in a set measurable**T**. Thus ,since o (

**T**) s ro , every Borel set in the plane is measurable**T**. Q . E . D . In viewof Lemma 10 , it behooves us to seek conditions under which the points on I ,

which ...

Page 2160

It will next be shown that the vector x - y is in the closure of the manifold ( No I –

) X . To see this it will , in view of Corollary II . 3 . 13 , suffice to show that * ( x - y )

= 0 for every linear functional 3 * which vanishes on ( 101 –

It will next be shown that the vector x - y is in the closure of the manifold ( No I –

**T**) X . To see this it will , in view of Corollary II . 3 . 13 , suffice to show that * ( x - y )

= 0 for every linear functional 3 * which vanishes on ( 101 –

**T**) X . If x * is such a ...### What people are saying - Write a review

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