## 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

Then , since the collection of

bounded , it is clear from [ * ] that the collection of

T + P ) , n 2 K , is uniformly bounded . Moreover , Lan ( E ( An ; T ) – Elun ; T + P )

...

Then , since the collection of

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

**finite**sums of projections ElMn ;T + P ) , n 2 K , is uniformly bounded . Moreover , Lan ( E ( An ; T ) – Elun ; T + P )

...

Page 2469

8 ) is very smooth and

2 , then choose 8 = 8 ( e ) so that IV ( 1 , 8 ) – V ( n ) / * < € / 2 , and put y ( 8 ) = V (

1 , 0 ) – V , it follows that V + V ( E ) is very smooth and

8 ) is very smooth and

**finite**. If we now choose n = n ( e ) so that IV ( n ) – V * < € /2 , then choose 8 = 8 ( e ) so that IV ( 1 , 8 ) – V ( n ) / * < € / 2 , and put y ( 8 ) = V (

1 , 0 ) – V , it follows that V + V ( E ) is very smooth and

**finite**, and that | V ( 8 ) ...### What people are saying - Write a review

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