For the last decade there has been a generalized trend in mathematics on the search for
large algebraic structures (linear spaces, closed subspaces, or infinitely generated …

Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is
called lineable whenever A contains, except for zero, an infinite dimensional vector …

In this paper, weighted backward shift operators T w associated to a Schauder basis of a
Banach space are considered. These operators are emblematic in the setting of linear chaos …

We prove the spaceability of the set of hypercyclic vectors for shift-like operators. Shift-like
operators appear naturally as composition operators on L p (X), when the underlying space …

We study the spaceability of the set of recurrent vectors for an operator on a Banach space.
In particular, we find sufficient conditions for a quasi-rigid operator to have a recurrent …

Given a domain of holomorphy D in ℂ N, N≥ 2, we show that the set of holomorphic
functions in D whose cluster sets along any finite length paths to the boundary of D is …

The question of whether a hypercyclic operator T acting on a Fréchet algebra X admits or not
an algebra of hypercyclic vectors (but 0) has been addressed in the recent literature. In this …

We introduce the Banach spaces ℓ a, bp and c 0, a, b, of analytic functions on the unit disc,
having normalized Schauder bases consisting of polynomials of the form fn (z)=(an+ bnz) …

We show that several convolution operators on the space of entire functions, such as the
MacLane operator, support a dense hypercyclic algebra that is not finitely generated …

This paper is devoted to the study of typical properties (in the Baire Category sense) of
certain classes of continuous linear operators acting on Fr\'echet algebras, endowed with …