## Linear Operators: Spectral theory |

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Page 1092

6 LEMMA. Let T be a compact operator, and A, (T) an enumeration of its

eigenvalues, repeated according to multiplicity, and in decreasing order of

absolute values. (If there are only a

write A, (T) = 0 ...

6 LEMMA. Let T be a compact operator, and A, (T) an enumeration of its

eigenvalues, repeated according to multiplicity, and in decreasing order of

absolute values. (If there are only a

**finite**number N of non-zero eigenvalues, wewrite A, (T) = 0 ...

Page 1147

CoRollARy: If G is a compact topological group satisfying the second axiom of

countability, and G is not a

G is countable. A complete set of representations of a

CoRollARy: If G is a compact topological group satisfying the second axiom of

countability, and G is not a

**finite**set, then any complete set of representations ofG is countable. A complete set of representations of a

**finite**group is**finite**.Page 1908

Nelson Dunford, Jacob T. Schwartz. Fréchet differential, definition, (92) theory for

compact operators, VII.4 Fredholm alternative, (609–610) Fubini theorem, for

general

, ...

Nelson Dunford, Jacob T. Schwartz. Fréchet differential, definition, (92) theory for

compact operators, VII.4 Fredholm alternative, (609–610) Fubini theorem, for

general

**finite**measure spaces, III.11.13 (193) for positive a-**finite**measure spaces, ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero