Coherence generation, symmetry algebras, and Hilbert space fragmentation

Symmetries of Hilbert space effect algebras

Let H be a Hilbert space and E(H) the effect algebra on H, that is, E(H) is the set of all self-adjoint operators A : H → H satisfying 0 ≤ A ≤ I. The effect algebra can be equipped with serveral operations and relations that are important in mathematical foundations of quantum mechanics. Automorphisms with respect to these operations or relations are called symmetries. We present a new method t...

Characterizations of the Automorphisms of Hilbert Space Effect Algebras

In this paper we characterize the automorphisms of Hilbert space effect algebras by means of their preserving properties which concern certain relations and quantities appearing in quantummeasurement theory.

A Morita Theorem for Algebras of Operators on Hilbert Space

We show that two operator algebras are strongly Morita equivalent (in the sense of Blecher, Muhly and Paulsen) if and only if their categories of operator modules are equivalent via completely contractive functors. Moreover, any such functor is completely isometrically isomorphic to the Haagerup tensor product (= interior tensor product) with a strong Morita equivalence bimodule. Date: Septembe...

Comparability preserving maps on Hilbert space effect algebras

We describe the general form of bijective comparability preserving transformations of the Hilbert space effect algebra, thus improving several known characterizations of ortho-order automorphisms.

Hilbert Algebras of Fractions