## 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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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero