## Linear Operators: Spectral theory |

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Page 1037

product clearly converges to zero for 1 = 2 it is readily seen that the function 9 ( T ) is

product clearly converges to zero for 1 = 2 it is readily seen that the function 9 ( T ) is

**analytic**for å + 0 and vanishes only for 2 in o ( T ) . It remains to show that if 1 # 0 , then qi ( T ) is continuous in T relative to the ...Page 1040

y ( a ) is

y ( a ) is

**analytic**even at a = rm . 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 2 = rom , so that y ( 2 ) can only fail to be**analytic**at the ...Page 1102

The determinant det ( 1 + zTn ) is an

The determinant det ( 1 + zTn ) is an

**analytic**( and even a polynomial ) function of z , if Tn operates in finite - dimensional space , and hence more generally if T , has a finite - dimensional range . Thus , since a bounded convergent ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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