Abstract
We develop a general theory of order isomorphisms of operator intervals. In this way we unify and extend several known results, among others the famous Ludwig’s description of ortho-order automorphisms of effect algebras and Molnár’s characterization of bijective order preserving maps on bounded observables. Besides proving several new results, one of the main contributions of the paper is to provide self-contained proofs of several known theorems whose original proofs depend on various deep results from functional analysis, operator algebras, and geometry. At the end we will show the optimality of the obtained theorems using Löwner’s theory of operator monotone functions.
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The author was supported by a grant from ARRS, Slovenia, Grant No. P1-0288.
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Šemrl, P. Order Isomorphisms of Operator Intervals. Integr. Equ. Oper. Theory 89, 1–42 (2017). https://doi.org/10.1007/s00020-017-2395-5
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DOI: https://doi.org/10.1007/s00020-017-2395-5