## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 1092

Let T be a compact operator , and 2n ( T ) an enumeration of its eigenvalues , repeated according to multiplicity , and in decreasing order of absolute values . ( If there are only a

Let T be a compact operator , and 2n ( 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 , we write ...Page 1147

COROLLARY : If G is a compact topological group satisfying the second axiom of countability , and G is not 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 of G is countable . A complete set of representations of a**finite**group ...Page 1460

Then , if r is

Then , if r is

**finite**below a , and the leading coefficient of + never vanishes , ttt , is**finite**below . PROOF . It is clear that we may suppose without loss of generality that a = 0. By Corollary 24 ( b ) , Corollary XII.4.13 ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### 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 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero