## Linear Operators: Spectral operators |

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Page 2292

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

limit point ; ( b ) the resolvent R ( d ; 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 ( d ; 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 2300

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. Then ,

since the collection of

it is clear from [ * ] that the collection of

2 ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. Then ,

since the collection of

**finite**sums of projections E ( Nn ; T ) is uniformly bounded ,it is clear from [ * ] that the collection of

**finite**sums of projections ElMn ; T + P ) , n2 ...

Page 2469

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

there exists an integer n such that f : ( a ) = 0 for i > n ; ( ii ) for 1 sisn , we have f : (

a ) = 0 if a ly . Moreover , there exists a function fi defined on R which is infinitely ...

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

**finite**if ( i )there exists an integer n such that f : ( a ) = 0 for i > n ; ( ii ) for 1 sisn , we have f : (

a ) = 0 if a ly . Moreover , there exists a function fi defined on R which is infinitely ...

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