## Linear Operators, Part 2 |

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Page 1033

111 1212 Thus , the function g ( 2 ) / 22 is

immediately that g has the Laurent expansion až + b + + ... 2 in the neighborhood

of 2 = 0. Consequently , the

111 1212 Thus , the function g ( 2 ) / 22 is

**analytic**and vanishes at i = 0. It followsimmediately that g has the Laurent expansion až + b + + ... 2 in the neighborhood

of 2 = 0. Consequently , the

**analytic**function g ( 1 ) -ai is**analytic**for all finite ...Page 1040

yı ( ) is

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

that y ( 2 ) can only fail to be

yı ( ) is

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

**analytic**at all the points a = hm , sothat y ( 2 ) can only fail to be

**analytic**at the point i = 0. To show this , note that ...Page 1102

The determinant det ( I + zT , ) 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 + zT , ) 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 ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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