On decomposable semigroups and applications

Non-Decomposable Quantum Dynamical Semigroups and Bound Entangled States

We use open quantum system techniques to construct one-parameter semigroups of positive maps and apply them to study the entanglement properties of a class of 16-dimensional density matrices, representing states of a 4× 4 bipartite system.

On Extensions over Semigroups and Applications

Applying a theorem according to Rhemtulla and Formanek, we partially solve an open problem raised by Hochman with an affirmative answer. Namely, we show that if G is a countable torsion-free locally nilpotent group that acts by homeomorphisms on X, and S ⊂ G is a subsemigroup not containing the unit of G such that f ∈ 〈1, s f : s ∈ S〉 for every f ∈ C(X), then (X, G) has zero topological entropy.

Profinite semigroups and applications∗

Profinite semigroups may be described shortly as projective limits of finite semigroups. They come about naturally by studying pseudovarieties of finite semigroups which in turn serve as a classifying tool for rational languages. Of particular relevance are relatively free profinite semigroups which for pseudovarieties play the role of free algebras in the theory of varieties. Combinatorial pro...

Structure and Applications of Totally Decomposable Metrics

Generalized Mehler semigroups and applications

We construct and study generalized Mehler semigroups (pt)t≥0 and their associated Markov processes M. The construction methods for (pt)t≥0 are based on some new purely functional analytic results implying, in particular, that any strongly continuous semigroup on a Hilbert space H can be extended to some larger Hilbert space E, with the embedding H ⊂ E being Hilbert-Schmidt. The same analytic ex...