Displaying similar documents to “Norms of hypercyclic sequences.”

G-narrow operators and G-rich subspaces

Tetiana Ivashyna (2013)

Open Mathematics

Similarity:

Let X and Y be Banach spaces. An operator G: X → Y is a Daugavet center if ‖G +T‖ = ‖G‖+‖T‖ for every rank-1 operator T. For every Daugavet center G we consider a certain set of operators acting from X, so-called G-narrow operators. We prove that if J is the natural embedding of Y into a Banach space E, then E can be equivalently renormed so that an operator T is (J ○ G)-narrow if and only if T is G-narrow. We study G-rich subspaces of X: Z ⊂ X is called G-rich if the quotient map q:...

Small sets and hypercyclic vectors

Frédéric Bayart, Étienne Matheron, Pierre Moreau (2008)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We study the ``smallness'' of the set of non-hypercyclic vectors for some classical hypercyclic operators.