## 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 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 1460

Then , if r is

, is

that 2 = 0 . By Corollary 24 ( b ) , Corollary XII . 4 . 13 , and Corollary 26 , To ( t ) ...

Then , if r is

**finite**below 2 , and the leading coefficient of ott , never vanishes , t + t, is

**finite**below 2 . Proof . It is clear that we may suppose without loss of generalitythat 2 = 0 . By Corollary 24 ( b ) , Corollary XII . 4 . 13 , and Corollary 26 , To ( t ) ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 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 adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero