Paschke’s version of Stinespring’s theorem associates a Hilbert C∗-module along with a generating vector to every completely positive map. Building on this, to every quantum dynamical semigroup (QDS) on a C∗-algebra 𝒜 one may associate an inclusion system E=(Et) of Hilbert 𝒜-𝒜-modules with a generating unit ξ=(ξt). Suppose ℬ is a von Neumann algebra, consider M2(ℬ), the von Neumann algebra of 2×2

We introduce an infinite-dimensional p-adic affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However, it is possible to define its action on some classes of functions.

We prove that every stationary state in the annihilator of all Kraus operators of a weak coupling limit-type Markov generator consists of two pieces, one of them supported on the interaction-free subspace and the second one on its orthogonal complement. In particular, we apply the previous result to describe in detail the structure of a slightly modified quantum transport model due to Arefeva et al

Let X be a separable Banach space endowed with a non-degenerate centered Gaussian measure μ. The associated Cameron–Martin space is denoted by H. Consider two sufficiently regular convex functions U:X→ℝ and G:X→ℝ. We let ν=e−Uμ and Ω=G−1(−∞,0]. In this paper, we study the domain of the self-adjoint operator associated with the quadratic form (ψ,φ)↦∫Ω∇Hψ,∇HφHdνψ,φ∈W1,2(Ω,ν),(0.1) and we give sharp embedding

In this paper we prove, for small Hurst parameters, the higher-order differentiability of a stochastic flow associated with a stochastic differential equation driven by an additive multi-dimensional fractional Brownian noise, where the bounded variation part is given by the local time of the unknown solution process. The proof of this result relies on Fourier analysis-based variational calculus techniques

For non-anticipative functionals, differentiable in Chitashvili’s sense, the Itô formula for cadlag semimartingales is proved. Relations between different notions of functional derivatives are established.

In this paper, we study the self-intersection local times of multifractional Brownian motion (mBm) in higher dimensions in the framework of white noise analysis. We show that when a suitable number of kernel functions of self-intersection local times of mBm are truncated then we obtain a Hida distribution. In addition, we present the expansion of the self-intersection local times in terms of Wick powers