Related papers: Non power bounded generators of strongly continuou…

Let $A$ be a Banach algebra with a bounded left approximate identity $\{e_\lambda\}_{\lambda\in\Lambda}$, let $\pi$ be a continuous representation of $A$ on a Banach space $X$, and let $S$ be a non-empty subset of $X$ such that…

We identify the semigroups consisting of bounded composition operators on the Hardy spaces $H^p(\U)$ of the upper half-plane. We show that any such semigroup is strongly continuous on $H^p(\U)$ but not uniformly continuous and we identify…

This paper provides a complete characterization of quasicontractive $C_0$-semigroups on Hardy and Dirichlet space with a prescribed generator of the form $Af=Gf'$. We show that such semigroups are semigroups of composition operators and we…

The following natural question arises from Shalom's innovational work (1999, Publ. IHES): "Can we establish an intrinsic criterion to synthesize relative fixed point properties into the whole fixed point property without assuming Bounded…

Given a Hilbert space and the generator $A$ of a strongly continuous, exponentially stable, semigroup on this Hilbert space. For any $g(-s) \in {\mathcal H}_{\infty}$ we show that there exists an infinite-time admissible output operator…

We show that, given a Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded)…

The discrete Ces\`aro operator $\mathsf{C}$ is investigated in the class of power series spaces $\Lambda_0(\alpha)$ of finite type. Of main interest is its spectrum, which is distinctly different when the underlying Fr\'echet space…

Given $T_1,\dots, T_n$ commuting power-bounded operators on a Banach space we study under which conditions the equality $\ker (T_1-\mathrm{I})\cdots (T_n-\mathrm{I})=\ker(T_1-\mathrm{I})+\cdots +\ker (T_n-\mathrm{I})$ holds true. This…

If X is a sequentially complete locally convex space, then a quotient bounded operator T is regular (in the sense of Waelbroeck) if and only if it is a bounded element (in the sense of Allan) of the algebra of quotient bounded operators on…

We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis…

We investigate rates of decay for $C_0$-semigroups on Hilbert spaces under assumptions on the resolvent growth of the semigroup generator. Our main results show that one obtains the best possible estimate on the rate of decay, that is to…

We give a simple, straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator $A$ in a complex Hilbert space as well as of the collection $\left\{e^{tA}\right\}_{t\ge 0}$ of its exponentials, which,…

Consider the lattice of bounded linear operators on the space of Borel measures on a Polish space. We prove that the operators which are continuous with respect to the weak topology induced by the bounded measurable functions form a…

Necessary and sufficient conditions are presented for the Abel averages of discrete and strongly continuous semigroups, $T^k$ and $T_t$, to be power convergent in the operator norm in a complex Banach space. These results cover also the…

Consider $d$ commuting $C_{0}$-semigroups (or equivalently: $d$-parameter $C_{0}$-semigroups) over a Hilbert space for $d \in \mathbb{N}$. In the literature (\textit{cf.} [29, 26, 27, 23, 18, 25]), conditions are provided to classify the…

We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided L\'evy processes. On one hand this allows modellers to use appropriate boundary conditions with confidence when restricting…

Averaged operators have played an important role in fixed point theory in Hilbert spaces. They emerged as a necessity to obtain solutions to fixed point problems where the underlying operator is not contractive and thus renders Banach fixed…

For nonuniform exponentially bounded evolution families on the half-line we introduce a class of Banach function spaces on which we define nonuniform evolution semigroups. We completely characterize nonuniform exponential stability in terms…

A sequence in a $C^*$-algebra $A$ is called completely Sidon if its span in $A$ is completely isomorphic to the operator space version of the space $\ell_1$ (i.e. $\ell_1$ equipped with its maximal operator space structure). The latter can…

The Stokes equation on a domain $\Omega \subset R^n$ is well understood in the $L^p$-setting for a large class of domains including bounded and exterior domains with smooth boundaries provided $1<p<\infty$. The situation is very different…