## Linear Operators, Part 2 |

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Page 1040

y ( 2 ) is

R ( ā ; T ) * y vanishes which will prove that y ( a ) is

rm , so that y ( 2 ) can only fail to be

...

y ( 2 ) is

**analytic**even at a = hm . It will now be shown that y ( 2 ) = 2N Elām ; T ) *R ( ā ; T ) * y vanishes which will prove that y ( a ) is

**analytic**at all the points 2 =rm , so that y ( 2 ) can only fail to be

**analytic**at the point à = 0 . To show this , note...

Page 1102

The determinant det ( I + zTn ) is an

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

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

of ...

The determinant det ( I + zTn ) is an

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

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

of ...

Page 1364

It follows by induction that we can construct the required functionals 91 , . . . , 9n

in K . We now select a neighborhood G ( 20 ) of 2o such that the

9 ; Q ; ( 2 ) } has a non - vanishing determinant for de G ( 2o ) . It follows easily

that ...

It follows by induction that we can construct the required functionals 91 , . . . , 9n

in K . We now select a neighborhood G ( 20 ) of 2o such that the

**analytic**matrix {9 ; Q ; ( 2 ) } has a non - vanishing determinant for de G ( 2o ) . It follows easily

that ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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