## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1083

... an analytic function of 1 , even if we regard it as having values in the space HS

of operators of Hilbert - Schmidt class . Consequently , the series 4 ( 2 ) — 28 ( 2 )

1 = 24 , 2n of the preceding

... an analytic function of 1 , even if we regard it as having values in the space HS

of operators of Hilbert - Schmidt class . Consequently , the series 4 ( 2 ) — 28 ( 2 )

1 = 24 , 2n of the preceding

**exercise**converges in the Hilbert - Schmidt norm .Page 1086

Show , finally , that by choosing A ( 8,8 ) 0 for all s in S , we obtain the result of

method of

of trace ...

Show , finally , that by choosing A ( 8,8 ) 0 for all s in S , we obtain the result of

**Exercise**46 as a special case of the present result . ( Hint : Generalize themethod of

**Exercise**46. ) 49 The operator A of Hilbert - Schmidt class is said to beof trace ...

Page 1087

( Hint : For ( d ) , use Weyl's inequality ,

50 ( Halberg ) Let ( S , E , u ) be a o - finite measure space . Let T , be a 1 -

parameter family of bounded operators defined in a subinterval I of the parameter

...

( Hint : For ( d ) , use Weyl's inequality ,

**Exercise**30. ) E. Miscellaneous Erercises50 ( Halberg ) Let ( S , E , u ) be a o - finite measure space . Let T , be a 1 -

parameter family of bounded operators defined in a subinterval I of the parameter

...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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