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 …

We first generalize the results of León-Saavedra and Müller (2006)[10] on hypercyclic
subspaces to sequences of operators on Fréchet spaces with a continuous norm. Then we …

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 …

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Known results about hypercyclic subspaces concern either Fréchet spaces with a
continuous norm or the space ω. We fill the gap between these spaces by investigating …

A Fréchet space X satisfies the Hereditary Invariant Subspace (resp. Subset) Property if for
every closed infinite-dimensional subspace M in X, each continuous operator on M …

We unify the recently developed abstract theories of universal series and extended universal
series to include sums of the form ∑ _ k= 0^ n a_k x_ n, k∑ k= 0 nakxn, k for given …

Let (λ k) k≥ 1 be countably many increasing sequences of integers tending to∞. For a
power series f=∑ iaizi, we denote by S n (f)=∑ i= 0 naizi the n th partial sum of f. Under …

In this note, the universality of a sequence of operators associated to the partial sums of the
Taylor series of a holomorphic function is investigated. The emphasis is put on the fact that …

We exhibit the first examples of Fréchet spaces which contain a closed infinite dimensional
subspace of universal series, but no restricted universal series. We consider classical …