## Linear Operators: Spectral theory |

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Page 1040

yı ( 2 ) is

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

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

yı ( 2 ) is

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

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

**analytic**at the point a 0. To show this ...Page 1102

The determinant det ( 1 + zTn ) is an

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

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

The determinant det ( 1 + zTn ) is an

**analytic**( and even a polynomial ) function of2 , if Tn operates in finite - dimensional space , and hence more generally if T ,

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

Page 1364

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

R. We now select a neighborhood G ( 20 ) of lo such that the

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

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

R. We now select a neighborhood G ( 20 ) of lo such that the

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

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

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