## Linear Operators: Spectral operators |

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Page 2241

These equations show that T ( f ) and T ( 1 / f ) are one - to - one operators and

that the range of T ( f ) is a

in D ( T ( f ) ) , then x = T ( 1 / f ) T ( f ) x , and so x is in the range R ( T ( 1 / f ) ) of T

...

These equations show that T ( f ) and T ( 1 / f ) are one - to - one operators and

that the range of T ( f ) is a

**subset**of the domain of T ( 1 / f ) and vice versa . If x isin D ( T ( f ) ) , then x = T ( 1 / f ) T ( f ) x , and so x is in the range R ( T ( 1 / f ) ) of T

...

Page 2256

Since o ( T ) is totally disconnected , each point , in o ( T ) is contained in an

arbitrarily small compact

of o ( T ' ) . It follows that the set 7 ( 0 ) = { z12 - 1€ 0 } is a compact

) ...

Since o ( T ) is totally disconnected , each point , in o ( T ) is contained in an

arbitrarily small compact

**subset**o of o ( T ) which is open in the relative topologyof o ( T ' ) . It follows that the set 7 ( 0 ) = { z12 - 1€ 0 } is a compact

**subset**of o ( R) ...

Page 2257

3 that E ( 0 ; T ) = E ( + ( 0 ) ; R ) for each compact spectral set o of T . Moreover , it

is clear that as o runs over the family K of all compact open

) runs over the family of all compact open

3 that E ( 0 ; T ) = E ( + ( 0 ) ; R ) for each compact spectral set o of T . Moreover , it

is clear that as o runs over the family K of all compact open

**subsets**of o ( T ) , t ( o) runs over the family of all compact open

**subsets**of o ( R ) which do not ...### What people are saying - Write a review

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