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Order automorphisms of effect algebras

Peter Semrl

Abstract

An elegant description of the general form of order automorphisms of effect algebras has been known in the complex case. We present a much simpler proof based on the projective geometry which works also in the real case. As an application we classify order isomorphic pairs of matrix intervals and describe the general form of order isomorphisms for any pair of isomorphic matrix intervals.

Order automorphisms of effect algebras

Abstract

An elegant description of the general form of order automorphisms of effect algebras has been known in the complex case. We present a much simpler proof based on the projective geometry which works also in the real case. As an application we classify order isomorphic pairs of matrix intervals and describe the general form of order isomorphisms for any pair of isomorphic matrix intervals.
Paper Structure (5 sections, 15 theorems, 160 equations)

This paper contains 5 sections, 15 theorems, 160 equations.

Table of Contents

  1. Introduction
  2. Preliminary results
  3. Order automorphisms of $[0,I]$
  4. Two-dimensional case
  5. Order isomorphisms of matrix intervals

Key Result

Lemma 2.1

Let $A,B \in S(H)$ be positive. Then the following two statements are equivalent.

Theorems & Definitions (24)

  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • proof
  • ...and 14 more