Related papers: Contraction semigroups on $L_\infty({\bf R})$

Using recent developments on locally compact groups, we are able to obtain quantitative results on embeddings into Lebesgue spaces for a large class of HNN extensions.

It is shown how to construct *-homomorphic quantum stochastic Feller cocycles for certain unbounded generators, and so obtain dilations of strongly continuous quantum dynamical semigroups on C* algebras; this generalises the construction of…

Let $G$ be a linear algebraic group over a field $k$ of characteristic 0. We show that any two connected semisimple $k$-subgroups of $G$ that are conjugate over an algebraic closure of $k$ are actually conjugate over a finite field…

We prove that any weak* continuous semigroup $(T_t)_{t \geq 0}$ of factorizable Markov maps acting on a von Neumann algebra $M$ equipped with a normal faithful state can be dilated by a group of Markov $*$-automorphisms analogous to the…

Non-discrete semigroup $T_1$-topologies on the extended bicyclic semigroup $\mathscr{C}_\mathbb{Z}$ are constructed. Also, we present topological conditions, when a semigroup (shift-continuous) $T_1$-topology on $\mathscr{C}_\mathbb{Z}$ is…

Suppose $G$ is a finitely presented group that is hyperbolic relative to ${\bf P}$ a finite collection of 1-ended finitely generated proper subgroups of $G$. If $G$ and the ${\bf P}$ are 1-ended and the boundary $\partial (G,{\bf P})$ has…

Assume that a block operator of the form $\left(\begin{smallmatrix}A_{1}\\A_{2}\quad 0\end{smallmatrix}\right)$, acting on the Banach space $X_{1}\times X_{2}$, generates a contraction $C_{0}$-semigroup. We show that the operator $A_{S}$…

Two extension problems are solved. First, the class of locally matricial algebras over an arbitrary field is closed under extensions. Second, the class of locally finite dimensional semisimple algebras over a fixed field is closed under…

Let K be any compact set. The C^*-algebra C(K) is nuclear and any bounded homomorphism from C(K) into B(H), the algebra of all bounded operators on some Hilbert space H, is automatically completely bounded. We prove extensions of these…

We study growth rates for strongly continuous semigroups. We prove that a growth rate for the resolvent on imaginary lines implies a corresponding growth rate for the semigroup if either the underlying space is a Hilbert space, or the…

Let $F$ be a totally real field unramified at all places above $p$ and $D$ be a quaternion algebra which splits at either none, or exactly one, of the infinite places. Let $\bar{r}:\mathrm{Gal}(\bar{F}/F)\to…

Let $\mathcal{X}$ be a real separable Hilbert space. Let $C$ be a linear, bounded and positive operator on $\mathcal{X}$ and let $A$ be the infinitesimal generator of a strongly continuous semigroup on $\mathcal{X}$. Let $\{W(t)\}_{t\geq…

It is well known that weakly continuous semigroups defined over $\mathbb{R}_{+}$ are automatically strongly continuous. We extend this result to more generally defined semigroups, including multiparameter semigroups.

In this paper we establish generation of analytic strongly continuous semigroup in $L^p$--spaces for the symmetric matrix Schr\"odinger operator $div(Q\nabla u)-Vu$, where, for every $x\in\mathbb{R}^d$, $V(x)=(v_{ij}(x))$ is a semi-definite…

If a finitely generated torsion free group K has the property that all finitely generated subgroups S of K are either small or have growth constant bounded uniformly away from 1 then a non proper HNN extension G of K, that is a semidirect…

Form methods are most efficient to prove generation theorems for semigroups but also for proving selfadjointness. So far those theorems are based on a coercivity notion which allows the use of the Lax-Milgram Lemma. Here we consider weaker…

Let $P \subset \mathbb{R}^{d}$ be a closed convex cone. Assume that $P$ is pointed, i.e. the intersection $P \cap -P=\{0\}$ and $P$ is spanning, i.e. $P-P=\mathbb{R}^{d}$. Denote the interior of $P$ by $\Omega$. Let $E$ be a product system…

The goal of this survey is to describe some recent results concerning the L 2 extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity properties. The results presented here are…

In this paper we study a notion of HL-extension (HL standing for Herwig--Lascar) for a structure in a finite relational language $\mathcal{L}$. We give a description of all finite minimal HL-extensions of a given finite…

We extend some classical results of Cowling and Meda to the noncommutative setting. Let $(T_t)_{t>0}$ be a symmetric contraction semigroup on a noncommutative space $L_p(\mathcal{M}),$ and let the functions $\phi$ and $\psi$ be regularly…