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math.FA2026
Banach's principle in vector lattices
Alexander Dobrick
We develop an abstract Banach principle in vector lattices and apply it to obtain lattice-theoretic versions of the individual and maximal ergodic theorems, without recourse to any…
math.FA2024
Ultra Feller operators from a functional analytic perspective
Alexander Dobrick, Julian Hölz, Markus Kunze
It is a widely acknowledged fact that the product of two positive strong Feller operators on a Polish space enjoys the ultra Feller property. We present a functional analytic p…
math.FA2024
Uniform convergence of solutions to stochastic hybrid models of gene regulatory networks
Alexander Dobrick, Julian Hölz
In a recent paper by Kurasov, Lück, Mugnolo and Wolf, a hybrid gene regulatory network was proposed to model gene expression dynamics by using a stochastic system of coupled parti…