## Linear Operators: Spectral theory |

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Page 1455

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

and whose essential spectrum 04 ( T ) does not intersect the interval ( - 00 , 2 ) of

the real axis , we say that T is

formal ...

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

and whose essential spectrum 04 ( T ) does not intersect the interval ( - 00 , 2 ) of

the real axis , we say that T is

**finite**below a . ( b ) If i is a formally symmetricformal ...

Page 1459

A formally positive formally symmetric formal differential operator t is

zero . PROOF . It is obvious from Definition 20 that t is bounded below . Thus the

present corollary follows from Corollary 7 and Definition 25 ( b ) . Q . E . D . 31 ...

A formally positive formally symmetric formal differential operator t is

**finite**belowzero . PROOF . It is obvious from Definition 20 that t is bounded below . Thus the

present corollary follows from Corollary 7 and Definition 25 ( b ) . Q . E . D . 31 ...

Page 1460

Then , if t is

+ ry is

generality that 2 = 0 . By Corollary 24 ( b ) , Corollary XI1 . 4 . 13 , and Corollary

26 , To ...

Then , if t is

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

**finite**below 2 . Proof . It is clear that we may suppose without loss ofgenerality that 2 = 0 . By Corollary 24 ( b ) , Corollary XI1 . 4 . 13 , and Corollary

26 , To ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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