A trace class operator inequality (Q864660)
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scientific article; zbMATH DE number 5124046
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A trace class operator inequality |
scientific article; zbMATH DE number 5124046 |
Statements
A trace class operator inequality (English)
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12 February 2007
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The author extends the trace inequality \(\text{tr}[(AB)^n]\leq(\text{tr\,}A)^n (\text{tr\,}B)^n\), \(\forall n\in\mathbb{N}\), known for positive semidefinite matrices, to positive trace class Hilbert space operators \(A,B\). The proof is based on simultaneous approximation of \(A\) and \(B\) by finite-dimensional operators.
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Hilbert space
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positive trace class operator
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inequality
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