Guided by the construction of the unital *-algebra of closed operators which are ‘affiliated’ with a given unital *-algebra, we introduce the notion of the ‘monotone closure’ for certain increasing sequences of unital *-algebras. Then we study an example of a unital *-algebra F0(A) constructed from a countable number of copies of a unital *-algebra A. We endow F0(A) with a quantum semigroup str...

We call a semigroup compactification T of a (discrete) semigroup S Boolean if the underlying space of T is zero-dimensional. The class of Boolean compactifications of S is a complete lattice, in a natural way. Motivated by Numakura’s theoerem, we prove that this lattice is isomorphic to the ideal lattice of the lattice of finite congruence relations of S. We describe in some detail the lattice ...

In a recent work we have found a contraction semigroup able to correctly approximate a projected and perturbed one-parameter group of isometries in a generic Banach space, in the limit of weak-coupling. Here we study its generator by specializing toW ∗-algebras: after defining a Physical Subsystem in terms of a completely positive projecting conditional expectation, we find that it generates a ...

The families of right (left) translation finite subsets of a discrete infinite group Γ are defined and shown to be ideals. Their kernels ZR and ZL are identified as the closure of the set of products pq (p · q) in the Čech-Stone compactification βΓ. Consequently it is shown that the map π : βΓ → Γ , the canonical semigroup homomorphism from βΓ onto Γ , the universal semitopological semigroup co...

Statistically interpretable axioms are formulated that define a quantum stochastic process (QSP) as a causally ordered field in an arbitrary space–time region T of an open quantum system under a sequential observation at a discrete space-time localization. It is shown that to every QSP described in the weak sense by a self-consistent system of causally ordered correlation kernels there correspo...

Consider an effective Hamiltonian torus action T ×M → M on a topologically twisted, generalized complex manifold M of dimension 2n. We prove that the rank(T ) ≤ n − 2 and that the topological twisting survives Hamiltonian reduction. We then construct a large new class of such actions satisfying rank(T ) = n − 2, using a surgery procedure on toric manifolds.

We consider a class of evolution equations in Lindblad form, which model the dynamics of dissipative quantum mechanical systems with mean-field interaction. Particularly, this class includes the so-called Quantum Fokker-Planck-Poisson model. The existence and uniqueness of global-in-time, mass preserving solutions is proved, thus establishing the existence of a nonlinear conservative quantum dy...