We characterize disjoint hypercyclic and supercyclic tuples of unilateral Rolewicz-type operators on $c_0(\N)$ $\ell^p(\N)$, $p \in [1, \infty)$, which are a generalization the backward shift operator. show that hypercyclicity supercyclicity equivalent among subfamily these always satisfy Disjoint Hypercyclicity Criterion. also simultaneous \infty)$.

In this paper we give some sufficient conditions for the adjoint of the multiple weighted composition operators acting on some function spaces satisfying the Hypercyclicity Criterion. Mathematics Subject Classification: 47B37; 47B33

We extend the class of Banach sequence spaces constructed by Ledari, as presented in ''A class of hereditarily $ell_1$ Banach spaces without Schur property'' and obtain a new class of hereditarily $ell_p(c_0)$ Banach spaces for $1leq p<infty$. Some other properties of this spaces are studied.

A topological group G is h-complete if every continuous homomorphic image of G is (Ra˘ ıkov-)complete; we say that G is hereditarily h-complete if every closed subgroup of G is h-complete. In this paper, we establish open-map properties of hereditarily h-complete groups with respect to large classes of groups, and prove a theorem on the (total) minimality of sub-directly represented groups. Num...

We show that the product of a compact, sequential T2 space with an hereditarily absolutely countably compact T3 space is hereditarily absolutely countably compact, and further that the product of a compact T2 space of countable tightness with an hereditarily absolutely countably compact ω-bounded T3 space is hereditarily absolutely countably compact.

Even linear operators on infinite-dimensional spaces can display interesting dynamical properties and yield important links among functional analysis, differential and global geometry and dynamical systems, with a wide range of applications. In particular, hypercyclicity is an essentially infinite-dimensional property, when iterations of the operator generate a dense subspace. A Fréchet space a...

We will present some results and open problems on an extension of the Ackermann encoding of Hereditarily Finite Sets into Natural Numbers. In particular, we will introduce and discuss a simple modification of the above mentioned Ackermann encoding, that should naturally generalize from Hereditarily Finite Sets to Hereditarily Finite Hypersets.