## Linear operators: Spectral operators |

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Results 1-3 of 12

Page 2461

An operator V belonging to the

and B belong to the Hilbert-Schmidt class HS = c&2 , and where the Hilbert-

Schmidt norms \\A\\ and \[B\\ are both equal to the square root \V\{12 of the trace

norm ...

An operator V belonging to the

**trace class**^ can be factored as V = AB, where Aand B belong to the Hilbert-Schmidt class HS = c&2 , and where the Hilbert-

Schmidt norms \\A\\ and \[B\\ are both equal to the square root \V\{12 of the trace

norm ...

Page 2462

Moreover, ifC belongs to the

norm, and CT* converges to zero in trace norm. Proof. The set K = C({x e § [ |x| ^

1 }) is conditionally compact, and thus for each e > 0 there exists a finite set xlt ...

Moreover, ifC belongs to the

**trace class**<€x, then TnC converges to zero in tracenorm, and CT* converges to zero in trace norm. Proof. The set K = C({x e § [ |x| ^

1 }) is conditionally compact, and thus for each e > 0 there exists a finite set xlt ...

Page 2500

T; in a representation in which H1 is diagonal, S appears as an operation of

multiplication by an operator valued function / + T(x), where T(x) is an operator of

T; in a representation in which H1 is diagonal, S appears as an operation of

multiplication by an operator valued function / + T(x), where T(x) is an operator of

**trace class**for each x. Results concerning the scattering operator of the sort ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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