We review some of our results from the theory of product systems of Hilbert modules [BS00, BBLS00, Ske00a, Ske01, Ske02, Ske03]. We explain that the product systems obtained from a CP-semigroup in [BS00] and in [MS02] are commutants of each other. Then we use this new commutant technique to construct product systems from E0–semigroups on Ba(E) where E is a strongly full von Neumann module. (Thi...

We consider the Duhamel equation ? f = g in subspace C? xy {f ([0, 1] [0, 1]) : (x, y) F (xy) for some of space and prove that if pxy=0, 0, then this is uniquely solvable x y. The commutant restricted double integration operator Wxy := ?x 0 ?y (t?) d?dt on y also described. Some other related questions are discussed.

Many quantitative approaches to the dynamical scrambling of information in quantum systems involve study out-of-time-ordered correlators (OTOCs). In this paper, we introduce an algebraic OTOC ($\mathcal{A}$-OTOC) that allows us generalized subsystems under channels. For closed systems, framework was recently employed unify information-theoretic notions operator entanglement, coherence-generatin...