On order automorphisms of the effect algebra
Roman Drnov\v{s}ek
TL;DR
This paper provides simplified proofs of two descriptions of order automorphisms of the effect algebra, enhancing understanding of their structure by leveraging Molnár's characterization of positive operator automorphisms.
Contribution
It introduces concise proofs for existing formulas of effect algebra automorphisms, clarifying their structure using operator cone automorphism characterization.
Findings
Simplified proofs of Semrl's descriptions
Enhanced understanding of effect algebra automorphisms
Connections to positive operator cone automorphisms
Abstract
We give short proofs of two \v{S}emrl's descriptions of order automorphisms of the effect algebra. This sheds new light on both formulas that look quite complicated. Our proofs rely on Moln\'{a}r's characterization of order automorphisms of the cone of all positive operators.
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