## Linear Operators: Spectral theory |

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Page 1092

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

and an ( 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 an ( 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 , ife is

is

generality that a = 0 . By Corollary 24 ( b ) , Corollary X11 . 4 . 13 , and Corollary

26 , To ...

Then , ife is

**finite**below h , and the leading coefficient of ttty never vanishes , tttyis

**finite**below 2 . PROOF . It is clear that we may suppose without loss ofgenerality that a = 0 . By Corollary 24 ( b ) , Corollary X11 . 4 . 13 , and Corollary

26 , To ...

Page 1913

... Decomposition ) definition , III . 4 . 3 ( 126 )

extension of , III . 5 . 18 ( 143 ) as a metric space , III . 7 . 1 ( 158 ) , III . 9 . 6 ( 169 )

positive , III . 4 . 3 ( 126 ) product , of

11 .

... Decomposition ) definition , III . 4 . 3 ( 126 )

**finite**, III . 4 . 3 ( 126 ) Lebesgueextension of , III . 5 . 18 ( 143 ) as a metric space , III . 7 . 1 ( 158 ) , III . 9 . 6 ( 169 )

positive , III . 4 . 3 ( 126 ) product , of

**finite**number of**finite**measure spaces , III .11 .

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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additive adjoint operator Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero