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

Mathematical Physics 2017-11-10 v3 math.MP Operator Algebras Quantum Algebra Quantum Physics

Abstract

A quantum effect is an operator on a complex Hilbert space HH that satisfies 0AI0\leq A\leq I. We denote the set of all quantum effects by E(H){\cal E}(H). In this paper we prove, Theorem 4.3, on the theory of sequential product on E(H){\cal E}(H) which shows, in fact, that there are sequential products on E(H){\cal E}(H) which are not of the generalized L\"{u}ders form. This result answers a Gudder's open problem negatively.

Keywords

Cite

@article{arxiv.0812.0630,
  title  = {The Uniqueness Problem of Sequence Product on Operator Effect Algebra $\varepsilon (H)$},
  author = {Liu Weihua and Wu Junde},
  journal= {arXiv preprint arXiv:0812.0630},
  year   = {2017}
}
R2 v1 2026-06-21T11:47:47.083Z