## Linear Operators: Spectral theory |

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Page 1083

of the preceding

be a positive measure space. Then an operator A in the Hilbert space L2(S, 2, u)

is of Hilbert-Schmidt class if and only if there exists a uxu measurable function ...

of the preceding

**exercise**converges in the Hilbert-Schmidt norm. 44 Let (S, 2, u)be a positive measure space. Then an operator A in the Hilbert space L2(S, 2, u)

is of Hilbert-Schmidt class if and only if there exists a uxu measurable function ...

Page 1086

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

of

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

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

**Exercise**46.) 49 The operator A of Hilbert-Schmidt class is said to be of trace ...Page 1087

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

(Halberg) Let (S. 2, u) be a g-finite measure space. Let T, be a 1-parameter family

of bounded operators defined in a subinterval I of the parameter interval 1 < p ...

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

**Exercise**30.) E. Miscellaneous Earercises 50(Halberg) Let (S. 2, u) be a g-finite measure space. Let T, be a 1-parameter family

of bounded operators defined in a subinterval I of the parameter interval 1 < p ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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