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

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Page 2283

Then a projection E in B has

in B * has

* satisfy the countable chain condition . Also since each projection is the union ...

Then a projection E in B has

**finite**uniform multiplicity n if and only if its adjoint E *in B * has

**finite**uniform multiplicity n . PROOF . It is sufficient to suppose E and E* satisfy the countable chain condition . Also since each projection is the union ...

Page 2292

If T is discrete , then ( a ) its spectrum is a denumerable set of points with no

limit point ; ( b ) the resolvent R ( A ; T ) is compact for every 1 € 0 ( T ) ; ( c ) every

do in o ( T ) is a pole of

If T is discrete , then ( a ) its spectrum is a denumerable set of points with no

**finite**limit point ; ( b ) the resolvent R ( A ; T ) is compact for every 1 € 0 ( T ) ; ( c ) every

do in o ( T ) is a pole of

**finite**order vldo ) of the resolvent and if , for some ...Page 2469

Thus the proof of our lemma is complete . Q . E . D . Next we prove an important

inequality . 17 LEMMA . Suppose that we call on element f eH ' very smooth and

we ...

Thus the proof of our lemma is complete . Q . E . D . Next we prove an important

inequality . 17 LEMMA . Suppose that we call on element f eH ' very smooth and

**finite**if ( i ) there exists an integer n such that fi ( a ) = 0 for i > n ; ( ii ) for 1 şişn ,we ...

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