New nonexplosion conditions for Markov processes are derived from the general operator form of the conservativity condition for a quantum dynamical semigroup.

In this paper we study the robustness of strong stability of a discrete semigroup on a Hilbert space under bounded perturbations. As the main result we present classes of perturbations preserving the strong stability of the semigroup.

We show that the quantum family of all maps from a finite space to a finite dimensional compact quantum semigroup has a canonical quantum semigroup structure. Let X be a finite space and Y be a compact space. Then the space F (X,Y ) of all maps from X to Y , is a compact space with compact-open topology. The notion of quantum family of all maps, defined by Woronowicz [8] and Soltan [5], is a no...

For a von Neumann algebra M acting on a Hilbert space H with a cyclic and separating vector ξ0, we investigate the structure of Dirichlet forms on the natural standard form associated with the pair (M, ξ0). For a general Lindblad type generator L of a conservative quantum dynamical semigroup on M, we give sufficient conditions so that the operator H induced by L via the symmetric embedding of M...

In this paper we investigate the relation between discrete and continuous operators. More precisely, we investigate the properties of the semigroup generated by A, and the sequence Ad , n ∈ N, where Ad = (I +A)(I −A)−1. We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger...

We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain convolution operation: the latter maps a classical probability distribution on phase space and a quantum state to a quantum state. We show that this inequality a...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...