We specify the structure of completely positive operators and quantum Markov semigroup generators that are symmetric with respect to a family inner products, also providing new information on order extreme points in some previously studied cases.

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...

We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of cancellative semigroup, their convolution algebras, and tokens between them provides a common language for description of objects from these three fields.

We study Lp-theory of second order elliptic divergence type operators with measurable coefficients. To this end, we introduce a new method of constructing positive C0-semigroups on Lp associated with sesquilinear (not necessarily sectorial) forms in L2. A precise condition ensuring that the elliptic operator is associated with a quasi-contractive C0-semigroup on Lp is established.

In this paper, we prove the existence of mild solutions for the semilinear fractional order functional of VolterraFredholm type differential equations with nonlocal conditions in a Banach space. The results are obtained by using the theory of fractional calculus, the analytic semigroup theory of linear operators and the fixed point techniques. MSC: 34K37 • 34A08 • 47H10

A class of optimal control problems for infinite dimensional impulsive antiperiodic boundary value problem is considered. Using exponential stabilizability and discussing the impulsive evolution operators, without compactness and exponential stability of the semigroup governed by original principle operator, we present the existence of optimal controls. At last, an example is given for demonstr...

In many physical applications, the evolution of the system is endowed with dynamical boundary conditions, i.e., with boundary operators containing time derivatives. In this paper we discuss a generalization of such systems, where stochastic perturbations affect the way the system evolves in the interior of the domain as well as on the boundary. keywords: Stochastic differential equations, bound...

In this work we investigate semigroups of operators acting on noncommutative L-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and H∞ functional calculus. We discuss several examples of noncommutative diffusion semigroups. This includes Schur multipliers, q-Ornstein-Uhlenbeck semigroups, and the noncommutative Poiss...

It is shown that on certain Banach spaces, including C[0,1] and L1[0,1], there is no strongly continuous semigroup (Tt )0<t<1 consisting of weakly compact operators such that (Tt )0<t<1 is an R-bounded family. More general results concerning approximating sequences are included and some variants of R-boundedness are also discussed.  2004 Elsevier Inc. All rights reserved.

Trotter's product formula is given for nonlinear semigroups in L1 (fi^) generated by quasilinear operators of the form Aic)}^t^h'u, where \ + ■ ■ ■ + in L'fr?^).