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

A quantum effect is an operator on a complex Hilbert space $H$ that satisfies $0\le A\le I$. We denote the set of all quantum effects by $\mathcal{E}(H)$. In this paper we prove, Theorem 4.3, on the theory of sequential product on ${\cal E}(H)$whichshows,infact,thattherearesequentialproductson${\cal E}(H)$ which are not of the generalized L"{u}ders form. This result answers a Gudder’s open problem negatively.