## Linear Operators: General theory |

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Page 204

Since u ( Fn ) = Ss , tr ( $ a , Dua , ( dsa , ) does not converge to

Sin ( sq ) si it follows from the dominated convergence theorem ( 6 . 16 ) that

there is a point sa , in S , for which In ( $ 2 . ) is defined for all n and for which the

...

Since u ( Fn ) = Ss , tr ( $ a , Dua , ( dsa , ) does not converge to

**zero**and since oSin ( sq ) si it follows from the dominated convergence theorem ( 6 . 16 ) that

there is a point sa , in S , for which In ( $ 2 . ) is defined for all n and for which the

...

Page 232

Suppose that f ( 2 , 0 ) is not identically

and that the order of this

2 ( w ) , . . . , zk ( w ) in V , and these

Suppose that f ( 2 , 0 ) is not identically

**zero**but has a**zero**at some point zo in U ,and that the order of this

**zero**is m . ... w # 0 , f ( x , w ) has exactly k distinct**zeros**2 ( w ) , . . . , zk ( w ) in V , and these

**zeros**are given by fractional power series z ...Page 577

Let T be a compact operator , and let be a non -

one - to - one , the range of 21 - T is closed . Proof . Let y = limn - > Yn , where yn

= ( 21 – T ) xn . If the sequence { xn } contains a bounded subsequence , then ...

Let T be a compact operator , and let be a non -

**zero**complex number . If al - T isone - to - one , the range of 21 - T is closed . Proof . Let y = limn - > Yn , where yn

= ( 21 – T ) xn . If the sequence { xn } contains a bounded subsequence , then ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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