## Linear Operators: Spectral theory |

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Page 1040

It will now be shown that yz ( 2 ) = 2N Eām ; T ) * R ( ā ; T ) * y vanishes which will

prove that y ( 2 ) is

be

) ...

It will now be shown that yz ( 2 ) = 2N Eām ; T ) * R ( ā ; T ) * y vanishes which will

prove that y ( 2 ) is

**analytic**at all the points a = 2m , so that y ( 2 ) can only fail tobe

**analytic**at the point a = 0 . To show this , note that ( 42 ( 2 ) , x ) = ( 2 ^ Elām ; T) ...

Page 1102

The determinant det ( I + zT » ) is an

z , if T , operates in finite - dimensional space , and hence more generally if T ,

has a finite - dimensional range . Thus , since a bounded convergent sequence

of ...

The determinant det ( I + zT » ) is an

**analytic**( and even a polynomial ) function ofz , if T , operates in finite - dimensional space , and hence more generally if T ,

has a finite - dimensional range . Thus , since a bounded convergent sequence

of ...

Page 1379

If 0 ( • ) is

each Borel set e with compact closure contained in 1 . Thus , by Theorem 25 , 01

, . . . , Ox is a determining set for T . Q . E . D . 28 COROLLARY . Let T , 4 , 0 ; ...

If 0 ( • ) is

**analytic**for ; > k , it follows from Theorem 18 that psi ( e ) = 0 for j > k andeach Borel set e with compact closure contained in 1 . Thus , by Theorem 25 , 01

, . . . , Ox is a determining set for T . Q . E . D . 28 COROLLARY . Let T , 4 , 0 ; ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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