## Linear Operators, Part 2 |

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Page 1092

Nelson Dunford, Jacob T. Schwartz. 6 LEMMA . Let T be a compact operator ,

and in ( T ) an enumeration of its eigenvalues , repeated according to multiplicity ,

and in decreasing order of absolute values . ( If there are only a

of ...

Nelson Dunford, Jacob T. Schwartz. 6 LEMMA . Let T be a compact operator ,

and in ( T ) an enumeration of its eigenvalues , repeated according to multiplicity ,

and in decreasing order of absolute values . ( If there are only a

**finite**number Nof ...

Page 1460

Then , if t is

try is

generality that i = 0. By Corollary 24 ( b ) , Corollary XII.4.13 , and Corollary 26 , T.

( t ) ...

Then , if t is

**finite**below 1 , and the leading coefficient of t + tq never vanishes , Itry is

**finite**below 2 . PROOF . It is clear that we may suppose without loss ofgenerality that i = 0. By Corollary 24 ( b ) , Corollary XII.4.13 , and Corollary 26 , T.

( t ) ...

Page 1913

... ( 166 ) spaces of , III.7 , IV.2.15–17 ( 240 ) , IV.9 , IV.15 , ( 389–391 ) vector -

valued , study of , IV.10 ( 391 ) Measure space , decomposition of . ( See also

Decomposition ) definition , III.4.3 ( 126 )

of ...

... ( 166 ) spaces of , III.7 , IV.2.15–17 ( 240 ) , IV.9 , IV.15 , ( 389–391 ) vector -

valued , study of , IV.10 ( 391 ) Measure space , decomposition of . ( See also

Decomposition ) definition , III.4.3 ( 126 )

**finite**, III.4.3 ( 126 ) Lebesgue extensionof ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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