## Linear Operators: Spectral operators |

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Page 2150

Since the spectrum is totally disconnected , every spectral point is

spectral set of arbitrarily small diameter and thus in an S ( T ) set of arbitrarily

small diameter . Since it is clear that every subset of the resolvent set is an S ( T )

set ...

Since the spectrum is totally disconnected , every spectral point is

**contained**in aspectral set of arbitrarily small diameter and thus in an S ( T ) set of arbitrarily

small diameter . Since it is clear that every subset of the resolvent set is an S ( T )

set ...

Page 2234

The first statement follows from Definition 8 and the three paragraphs of

explanation which precede it , and from Lemma 6 . Statement ( i ) follows from

Corollary 7 . If e is a bounded Borel set with closure

supposed ...

The first statement follows from Definition 8 and the three paragraphs of

explanation which precede it , and from Lemma 6 . Statement ( i ) follows from

Corollary 7 . If e is a bounded Borel set with closure

**contained**in U , it may besupposed ...

Page 2256

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

arbitrarily small compact subset o of o ( T ) which is open in the relative topology

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

) ...

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

**contained**in anarbitrarily small compact subset o of o ( T ) which is open in the relative topology

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

) ...

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