We consider the Fröbenius-Perron semigroup of linear operators associated to a semidynamical system defined in a topological space X endowed with a finite or a σ -finite regular measure. We prove that if there exists a faithful invariant measure for the semidynamical system, then the Fröbenius-Perron semigroup of linear operators is C0-continuous in the space Lμ(X). We also give a geometrical c...

In this paper, we present a convergence rate analysis for the inexact Krasnosel’skĭı– Mann iteration built from nonexpansive operators. Our results include two main parts: we first establish global pointwise and ergodic iteration–complexity bounds, and then, under a metric subregularity assumption, we establish local linear convergence for the distance of the iterates to the set of fixed points...

We define continuous and inverse shadowing for flows and prove some properties. In particular, we will prove that an expansive flow without fixed points on a compact metric space which is a shadowing is also a continuous shadowing and hence an inverse shadowing (on a compact manifold without boundary).

In this paper we establish a result regarding the connection between continuous maximal regularity and generation of analytic semigroups on a pair of densely embedded Banach spaces. More precisely, we show that continuous maximal regularity for a closed operator A : E1 → E0 implies that A generates a strongly continuous analytic semigroup on E0 with domain equal E1.

We study dispersive mixed-order systems of pseudodifferential operators in the setting of Lp-Sobolev spaces. Under the weak condition of quasihyperbolicity, these operators generate a semigroup in the space of tempered distributions. However, if the basic space is a tuple of Lp-Sobolev spaces, a strongly continuous semigroup is in many cases only generated if p = 2 or n = 1. The results are app...

An absolutely continuous free semigroup algebra is weak-∗ type L. A free semigroup algebra is the wot-closed (nonself-adjoint, unital) algebra S generated by n isometries S1, . . . , Sn with pairwise orthogonal ranges. See [4] for an introduction. There is now a significant literature on these algebras [1, 2, 9, 10, 11, 7, 6, 8, 5, 16, 15, 18, 17, 20]. The prototype is the non-commutative Toepl...

Many important C∗-algebras, such as AF-algebras, Cuntz-Krieger algebras, graph algebras and foliation C∗-algebras, are the C∗-algebras of r-discrete groupoids. These C∗-algebras are often associated with inverse semigroups through the C∗-algebra of the inverse semigroup [HR90] or through a crossed product construction as in Kumjian’s localization [Kum84]. Nica [Nic94] connects groupoid C∗-algeb...

Given a finite set A and a distinguished function f : A −→ A , we study the set of all functions g : A −→ A that are continuous for all topologies for which f is continuous. The main result is a characterization of the functions f such that this set is trivial, that is, contains only the constant functions and the iterates of f . Introduction The Problem. Let A be a set and f : A → A be a fixed...