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Cobos, Fernando and Kühn, Thomas
(1989)
*On a Conjecture of Barry Simon on Trace Ideals.*
Duke mathematical journal , 59
(1).
pp. 295-299.
ISSN 0012-7094

Official URL: http://projecteuclid.org/euclid.dmj/1077307842

## Abstract

Let H denote a Hilbert space, T a compact operator on H, {sn(T)}1 n=1 the eigenvalues of |T|, and Sp (p > 0) the set of all such T for which {sn(T)}1 n=1 is in `p. If A and B are bounded linear operators on L2, say that B pointwise dominates A if |A(x)(t)| B(|x|)(t) a.e. for all x(t) in L2. It is known that if p = 2n for some positive integer n, B is in Sp, and B pointwise dominates A, then A is also in Sp. Simon has conjectured that this result fails for p < 2, and has given a counterexample for 0 < p 1. The authors provide a counterexample for the remaining cases where 1 < p < 2.

Item Type: | Article |
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Uncontrolled Keywords: | Trace ideals; compact operator; pointwise dominates |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 15609 |

Deposited On: | 13 Jun 2012 08:12 |

Last Modified: | 23 Oct 2013 16:12 |

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