## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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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 1459

Q.E.D. 30 COROLLARY . A formally positive formally symmetric formal differential

operator is

bounded below . Thus the present corollary follows from Corollary 7 and

Definition ...

Q.E.D. 30 COROLLARY . A formally positive formally symmetric formal differential

operator is

**finite**below zero . PROOF . It is obvious from Definition 20 that t isbounded below . Thus the present corollary follows from Corollary 7 and

Definition ...

Page 1460

Then , if t is

t , is

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

To ( t ) ...

Then , if t is

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

To ( t ) ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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