## Linear Operators, Part 2 |

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Page 1378

If the determining set 01 , . . . , One of Theorem 23 were known to be part of a

basis 01 , . . . , On with the properties of Theorem 13 , then the uniqueness of { Ô

is } would follow immediately from the

course ...

If the determining set 01 , . . . , One of Theorem 23 were known to be part of a

basis 01 , . . . , On with the properties of Theorem 13 , then the uniqueness of { Ô

is } would follow immediately from the

**preceding**theorem . Moreover , in thecourse ...

Page 1419

On the interval [ Si + 1 , mi + 1 ] , consider the two functions - f ( t ) and fi ( t ) = + | (

28i - 1 - t ) . We have ( - ) " = 9 ( - 1 ) , tí = quit , where qı ( t ) = 9 ( 28i - 1 - t ) 2 9 ( t )

, since q is monotone decreasing . By the

On the interval [ Si + 1 , mi + 1 ] , consider the two functions - f ( t ) and fi ( t ) = + | (

28i - 1 - t ) . We have ( - ) " = 9 ( - 1 ) , tí = quit , where qı ( t ) = 9 ( 28i - 1 - t ) 2 9 ( t )

, since q is monotone decreasing . By the

**preceding**lemma , - f ( t ) sti ( t ) in [ si ...Page 1771

... 0 . t > 0 , 62 , to PROOF . Statement ( i ) follows from the

Theorem 6 . 23 . Statement ( ii ) follows from statement ( ii ) of the

theorem , since a function satisfying the hypotheses of the present statement ...

... 0 . t > 0 , 62 , to PROOF . Statement ( i ) follows from the

**preceding**theorem andTheorem 6 . 23 . Statement ( ii ) follows from statement ( ii ) of the

**preceding**theorem , since a function satisfying the hypotheses of the present statement ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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