## Linear Operators: Spectral theory |

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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 1455

( a ) If T is a closed symmetric operator in Hilbert space which is bounded below

and whose essential spectrum ( T ) does not intersect the interval ( - 0 , 2 ) of the

real axis , we say that T is

( a ) If T is a closed symmetric operator in Hilbert space which is bounded below

and whose essential spectrum ( T ) does not intersect the interval ( - 0 , 2 ) of the

real axis , we say that T is

**finite**below a . ( b ) If į is a formally symmetric formal ...Page 1460

Then , if t is

ry is

generality that a = 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 1 + t never vanishes , r +ry is

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

, To ( t ) ...

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 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 |

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