## Linear Operators: Spectral theory |

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Page 1083

Consequently , the series O 4 ( 1 ) – 20 ( 2 ) 1 = 24 , 2 " n = 2 of the preceding

measure space . Then an operator A in the Hilbert space L2 ( S , E , p ) is of

Hilbert ...

Consequently , the series O 4 ( 1 ) – 20 ( 2 ) 1 = 24 , 2 " n = 2 of the preceding

**exercise**converges in the Hilbert - Schmidt norm . 44 Let ( S , E , u ) be a positivemeasure space . Then an operator A in the Hilbert space L2 ( S , E , p ) is of

Hilbert ...

Page 1086

Show , finally , that by choosing Ass , s ) = 0 for all s in S , we obtain the result of

method of

be of ...

Show , finally , that by choosing Ass , s ) = 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 tobe of ...

Page 1087

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

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**Exercises**50 ( Halberg ) Let ( S , E , u ) be a o - finite measure space . Let T , be a1 - parameter family of bounded operators defined in a subinterval I of the

parameter ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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