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

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Page 2160

It will next be

) 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 ...

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 ...

Page 2226

... bounded Boolean algebra of projections on X , then X has an equivalent norm

such that the functionals given by Lemma 3 . 12 can be expressed by means of a

semi - inner product . On the other hand , Walsh [ 2 ; p . 315 ) has

... bounded Boolean algebra of projections on X , then X has an equivalent norm

such that the functionals given by Lemma 3 . 12 can be expressed by means of a

semi - inner product . On the other hand , Walsh [ 2 ; p . 315 ) has

**shown**that in ...Page 2266

It will be

multiplicity on B , Lemma 2 permits us to restrict our attention to C . 5 LEMMA .

The set 6 is a dense o - ideal in B . A projection belongs to C if and only if it is the

carrier ...

It will be

**shown**that C is a dense o - ideal in B and thus , in defining themultiplicity on B , Lemma 2 permits us to restrict our attention to C . 5 LEMMA .

The set 6 is a dense o - ideal in B . A projection belongs to C if and only if it is the

carrier ...

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