Abstract

A quantum effect is an operator A on a complex Hilbert space H that satisfies is the set of all quantum effects on H. In 2001, Professors Gudder and Nagy studied the sequential product for . In 2005, Professor Gudder asked: Is the only sequential product on ? Recently, Liu and Wu have presented an example to show that the answer is negative. In this paper, first, we characterize some algebraic properties of the abstract sequential product on , second, we present a general method for constructing sequential products on and, finally, we study some properties of the sequential products constructed by the method.

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