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We use a method similar to ultraproducts to study the common fixed point of a left reversible semitopological semigroup acting on a Banach space. As an application, we prove a Bruck-type theorem for nearly uniformly convex Banach spaces to…
In this paper we study the robustness of strong stability of a discrete semigroup on a Hilbert space under bounded finite rank perturbations. As the main result we characterize classes of perturbations preserving the strong stability of the…
In this paper several joint spectra for a finite commuting family of closed operators in Banach space are considered, some new relations between these spectra established (earlier only the inclusion of the Taylor spectrum in the commutant…
We study properties of continuous semi-homogeneous operators of degree $k$ via various functions (e.g. measures of noncompactness) on all bounded subsets of a Banach space. We prove necessary and sufficient conditions for these functions to…
We establish spectral inclusion and mapping theorems for scalar type spectral operators, generalizing their counterparts for normal operators. Thereby, we extend a precise weak spectral mapping theorem, known to hold for $C_0$-semigroups of…
We characterize Banach spaces B of stable type p (1 < p < 2) by the property that for every sequence (X_i) of B-valued random variables, independent, centered and fulfilling some integrability assumption, the sequence S_n/n^(1/p) is a…
In this paper, we study stability of $M$-compactness for $l^p$ sum of Banach spaces for $1\leq p<\infty$. We also obtain a characterization of $M$-compact sets in terms of statistically maximizing sequence, a notion which is weaker than a…
In this note we study the differentiability with respect to the time-parameter of semigroups consisting of Lipschitzian or smooth self-mappings of a domain in a Banach space.
We prove an optimal result of stability under $\ell_p$-sums of some concentration properties for Lipschitz maps defined on Hamming graphs into Banach spaces. As an application, we give examples of spaces with Szlenk index arbitrarily high…
We study abstract sufficient criteria for open-loop stabilizability of linear control systems in a Banach space with a bounded control operator, which build up and generalize a sufficient condition for null-controllability in Banach spaces…
In this research project we presents the general properties, the spectral properties and the representation formulas for $C_0$-semigroups of linear operators in Banach spaces
In this note, we study some concentration properties for Lipschitz maps defined on Hamming graphs, as well as their stability under sums of Banach spaces. As an application, we extend a result of Causey on the coarse Lipschitz structure of…
We characterize the polynomial decay of orbits of Hilbert space $C_0$-semigroups in resolvent terms. We also show that results of the same type for general Banach space semigroups and functions obtained recently in the paper by C.J.K.Batty…
We give a characterization of a variation of constants type estimate relating two positive semigroups on (possibly different) $L_p$-spaces to one another in terms of corresponding estimates for the respective generators and of estimates for…
We study families of analytic semigroups, acting in a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parameter norm bounds using spectral properties of the respective…
In this paper we introduce a new notion of strong pseudo-amenability for Banach algebras. We study strong pseudo-amenability of some Matrix algebras. Using this tool, we characterize strong pseudo-amenability of $\ell^{1}(S)$, provided that…
Criteria for the stability of finite sections of a large class of convolution type operators on $L^p(\mathbb{R})$ are obtained. In this class almost all classical symbols are permitted, namely operators of multiplication with functions in…
We consider positive operator semigroups on ordered Banach spac\-es and study the relation of their long time behaviour to two different domination properties. First, we analyse under which conditions almost periodicity and mean ergodicity…
In this paper we provide spectral inclusion and mapping theorems for strongly continuous locally equicontinuous semigroups on Hausdorff locally convex spaces. Our results extend the classical spectral inclusion and mapping theorems for…
We establish criteria for the stability of the essential spectrum for unbounded operators acting in Banach modules. The applications cover operators acting on sections of vector fiber bundles over non-smooth manifolds or locally compact…