Hypercyclic and mixing operator semigroups

We describe a class of topological vector spaces admitting a mixing uniformly continuous operator group {T_t}_{t\in\C^n} with holomorphic dependence on the parameter $t$. This result covers those existing in the literature. We also describe a class of topological vector spaces admitting no supercyclic strongly continuous operator semigroups ${T_t}_{t\geq 0}$.Comment: arXiv admin note: text overlap with arXiv:0810.119

Multiplication Semigroups on Banach Function Spaces

In this paper we characterize multiplication operators induced by operator valued maps on Banach function spaces. We also study multiplication semigroups and stability of these operators.Comment: We want to withdraw the paper due to the paper needs a careful revision and some proper citations are to be provided. Also there are certain gaps in the results which need to be taken car

Endomorphisms of the lattice of epigroup varieties

We examine varieties of epigroups as unary semigroups, that is semigroups equipped with an additional unary operation of pseudoinversion. The article contains two main results. The first of them indicates a countably infinite family of injective endomorphisms of the lattice of all epigroup varieties. An epigroup variety is said to be a variety of finite degree if all its nilsemigroups are nilpotent. The second result of the article provides a characterization of epigroup varieties of finite degree in a language of identities and in terms of minimal forbidden subvarieties. Note that the first result is essentially used in the proof of the second one.Comment: In comparison with the previous version, we eliminate a few typos onl