Order isomorphisms on effect algebras of the C⁎-algebras of type [formula omitted

Abstract

Let A be a unital C⁎-algebra equipped with its natural order. As usual the effect algebra of A is the interval {a∈A:0≤a≤IA}, where IA denotes the unit of A. In this paper, we give a complete description of order isomorphisms between effect algebras of C⁎-algebras of type C(X)⊗B(H), where C(X) stands for the algebra of all continuous complex valued functions on a (non pathological) Hausdorff compact space X and B(H) denotes the algebra of all bounded linear operators on a complex Hilbert space H. Our results generalize some works by L. Molnár and P. Šemrl.