## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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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

Let R = T - 1 . Then , by Theorem VII . 9 . 5 , o ( R ) = { 212 - 1 € ( T ) } U { 0 } .

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 ' ) ...

Let R = T - 1 . Then , by Theorem VII . 9 . 5 , o ( R ) = { 212 - 1 € ( T ) } U { 0 } .

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 ' ) ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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