Related papers: The Hille-Yosida generation theorem for almost sur…

In this paper we prove a Hille-Yosida type theorem for relatively uniformly continuous positive semigroups on vector lattices. We introduce the notions of relatively uniformly continuous, differentiable, and integrable functions on…

We present and apply a theory of one parameter $C_0$-semigroups of linear operators in locally convex spaces. Replacing the notion of equicontinuity considered by the literature with the weaker notion of sequential equicontinuity, we prove…

We show that, for the $C_0$-semigroups of scalar type spectral operators, a well-known necessary condition for the generation of eventually norm-continuous $C_0$-semigroups, formulated exclusively in terms of the location of the spectrum of…

Using functional calculi theory, we obtain several estimates for $\|\psi(A)g(A)\|$, where $\psi$ is a Bernstein function, $g$ is a bounded completely monotone function and $-A$ is the generator of a holomorphic $C_0$-semigroup on a Banach…

In this paper, we first introduce the notion of a (mild) $C$-existence family in complete random normed modules, then we prove that a (mild) $C$-existence family can guarantee the existence of the (mild) solutions of the associated abstract…

We give a self-contained and streamlined exposition of a generation theorem for C0-semigroups based on the method of boundary triplets. We apply this theorem to port-Hamiltonian systems where we discuss recent results appearing in stability…

The goal of this paper is to establish fundamental properties of the Hochschild, topological Hochschild, and topological cyclic homologies of commutative, Noetherian rings, which are assumed only to be F-finite in the majority of our…

Let $G$ be a connected, simply connected, simple, complex, linear algebraic group. Let $P$ be an arbitrary parabolic subgroup of $G$. Let $X=G/P$ be the $G$-homogeneous projective space attached to this situation. Let $d\in H_2(X)$ be a…

In this paper we study the well-posedness of the evolution equation of the form $u'(t)=Au(t)+Cu(t)$, $t\ge 0$, where $A$ is the generator of a $C_0$- semigroup and $C$ is a (possibly unbounded) linear operator in a Banach space…

We present a short elementary proof of the Gearhart-Pr\"uss theorem for bounded $C_0$-semigroups on Hilbert spaces.

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…

Product systems are the classifying structures for semigroups of endomorphisms of B(H), in that two $E_0$-semigroups are cocycle conjugate iff their product systems are isomorphic. Thus it is important to know that every abstract product…

Let B be a sigma-unital C*-algebra. We show that every strongly continuous E_0-semigroup on the algebra of adjointable operators on a full Hilbert B-module E gives rise to a full continuous product system of correspondences over B. We show…

In this paper, we introduce notions of $J$-set near zero and $C$-set near zero for a dense subsemigroup of $((0,+\infty),+)$ and obtain some results for them. Also we derive the Central Sets Theorem near zero.

We study properties of continuous finite group actions on topological manifolds that hold true, for any finite group action, after possibly passing to a subgroup of index bounded above by a constant depending only on the manifold. These…

Given a $\Gamma$-semigroup $S$, we construct a semigroup $\Sigma$ in such a way that one sided ideals and quasi-ideals of $S$ can be regarded as one sided ideals and quasi-ideals respectively of $\Sigma$. This correspondence and other…

We improve on earlier results on the closure under free products of the class of automaton semigroups. We consider partial automata and show that the free product of two self-similar semigroups (or automaton semigroups) is self-similar (an…

We introduce almost cohomology groups for Lie rings definable in finite-dimensional theory. In particular, we define the 0th and 1st almost cohomology groups of a Lie ring module. Moreover, we prove that the 1st almost cohomology group of a…

It is folklore that a power bounded operator on a sequentially complete locally convex space generates a uniformly continuous $C_0$-semigroup which is given by the corresponding power series representation. Recently, Doma\'nski asked if in…

We present a generation theorem for positive semigroups on an $L^1$ space. It provides sufficient conditions for the existence of positive and integrable solutions of initial-boundary value problems. An application to a two-phase cell cycle…