Automorphisms of Hilbert space effect algebras

作者：Semrl Peter^*

来源：Journal of Physics A-Mathematical and Theoretical, 2015, 48(19): 195301.

DOI：10.1088/1751-8113/48/19/195301

• effect algebra
• ortho-order automorphism
• coexistency

Let H be a Hilbert space and E (H) the effect algebra on H. A bijective map phi: E(H) -> E(H) is called an ortho- order automorphism of E (H) if for every A, B is an element of E(H) we have A <= B double left right arrow phi(A) <= phi(B) and phi(A(perpendicular to)) = phi(A)(perpendicular to). The classical theorem of Ludwig states that every such phi is of the form phi(A) = UAU*, A is an element of E(H), for some unitary or antiunitary operator U. It is also known that each bijective map on E (H) preserving order and coexistency in both directions is of the same form. Can we improve these two theorems by relaxing the bijectivity assumption and/or replacing the above preserving properties by the weaker assumptions of preserving above relations in one direction only and still get the same conclusion? For both characterizations of automorphisms of effect algebras we will prove the optimal versions and give counterexamples showing the optimality of the obtained results.

• 出版日期2015-5-15