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

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 L\"{u}ders form. This result answers a Gudder's open problem negatively.