On equicontinuity and tightness of bi-continuous semigroups

  title={On equicontinuity and tightness of bi-continuous semigroups},
  author={Karsten Kruse and Felix L. Schwenninger},
  journal={Journal of Mathematical Analysis and Applications},

A note on the Lumer--Phillips theorem for bi-continuous semigroups

Given a Banach space X and an additional coarser Hausdorff locally convex topology τ on X we characterise the generators of τ -bi-continuous semigroups in the spirit of the Lumer–Phillips theorem,

Weighted composition semigroups on spaces of continuous functions and their subspaces

. This paper is dedicated to weighted composition semigroups on spaces of continuous functions and their subspaces. We consider semigroups induced by semiflows and semicocycles on Banach spaces F( Ω )

Linearisation of weak vector-valued functions

. We study the problem of linearisation of vector-valued functions which are defined in a weak way, e.g. weakly holomorphic or harmonic vector- valued functions. The two main approaches to such a

Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups

We consider final state observability estimates for bi-continuous semigroups on Banach spaces, i.e. for every initial value, estimating the state at a final time T > 0 by taking into account the

The abstract Cauchy problem in locally convex spaces

  • K. Kruse
  • Mathematics
    Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
  • 2022
We derive necessary and sufficient criteria for the uniqueness and existence of solutions of the abstract Cauchy problem in locally convex Hausdorff spaces. Our approach is based on a suitable notion

Sun dual theory for bi-continuous semigroups

. The sun dual space corresponding to a strongly continuous semi- group is a known concept when dealing with dual semigroups, which are in general only weak ∗ -continuous. In this paper we develop a



Continuity and equicontinuity of semigroups on norming dual pairs

We study continuity and equicontinuity of semigroups on norming dual pairs with respect to topologies defined in terms of the duality. In particular, we address the question whether continuity of a

A Hille-Yosida theorem for Bi-continuous semigroups

In order to treat one-parameter semigroups of linear operators on Banach spaces which are not strongly continuous, we introduce the concept of bi-continuous semigroups defined on Banach spaces with

Positive Desch--Schappacher perturbations of bi-continuous semigroups {on mathrmAM-spaces}

In this paper we consider positive Desch-Schappacher perturbations of bi-continuous semigroups on AM-spaces with an additional property concerning the additional locally convex topology. As an

On continuity properties of semigroups in real interpolation spaces

Starting from a bi-continuous semigroup in a Banach space X (which might actually be strongly continuous), we investigate continuity properties of the semigroup that is induced in real interpolation

Diffusion Semigroups in Spaces of Continuous Functions with Mixed Topology

Abstract We study transition semigroups and Kolmogorov equations corresponding to stochastic semilinear equations on a Hilbert space H . It is shown that the transition semigroup is strongly

Positive Miyadera–Voigt perturbations of bi-continuous semigroups

We discuss positive Miyadera–Voigt type perturbations for bi-continuous semigroups on $$\mathrm {AL}$$ AL -spaces with an additional locally convex topology generated by additive seminorms. The main

Mean ergodic theorems for bi-continuous semigroups

In this paper we study the main properties of the Cesàro means of bi-continuous semigroups, introduced and studied by Kühnemund (Semigroup Forum 67:205–225, 2003). We also give some applications to

A Pettis-type integral and applications to transition semigroups

Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition

Perturbations of Bi-continuous Semigroups with Applications to Transition Semigroups on Cb(H)

AbstractWe prove an unbounded perturbation theorem for bi-continuous semigroups on the space of bounded, continuous functions on the Hilbert space H. This is applied to the Ornstein-Uhlenbeck

Intermediate and extrapolated spaces for bi-continuous operator semigroups

We discuss the construction of the entire Sobolev (Hölder) scale for non-densely defined operators with rays of minimal growth on a Banach space. In particular, we give a construction for