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arXiv · 0812.0630

The Uniqueness Problem of Sequence Product on Operator Effect Algebra $\varepsilon (H)$

Liu Weihua·Wu Junde
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Abstract

A quantum effect is an operator on a complex Hilbert space $H$ that satisfies $0\leq A\leq I$. We denote the set of all quantum effects by ${\cal E}(H)$. In this paper we prove, Theorem 4.3, on the theory of sequential product on ${\cal E}(H)$ which shows, in fact, that there are sequential products on ${\cal E}(H)$ which are not of the generalized Lüders form. This result answers a Gudder's open problem negatively.

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BibTeXRIS

Liu Weihua, Wu Junde. 2009-04-22. The Uniqueness Problem of Sequence Product on Operator Effect Algebra $\varepsilon (H)$. https://doi.org/10.1088/1751-8113%2F42%2F18%2F185206

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