Hypercyclic Subspaces on Fréchet Spaces Without Continuous Norm

Operators with Common Hypercyclic Subspaces

We provide a reasonable sufficient condition for a family of operators to have a common hypercyclic subspace. We also extend a result of the third author and A. Montes [22], thereby obtaining a common hypercyclic subspace for certain countable families of compact perturbations of operators of norm no larger than one.

Additive functionals on spaces with non-absolutely-continuous norm

Invariant Subspaces for the Backward Shift on Hilbert Spaces of Analytic Functions with Regular Norm

We investigate the structure of invariant subspaces of backward shift operator Lf = (f − f(0))/ζ on a large class of abstract Hilbert spaces of analytic functions on the unit disc where the forward shift operator Mζf = ζf acts as a contraction. Our main results show that under certain regularity conditions on the norm of such a space, the functions in a nontrivial invariant subspace of L have m...

Existence theorems in linear chaos

Chaotic linear dynamics deals primarily with various topological ergodic properties of semigroups of continuous linear operators acting on a topological vector space. We treat the questions of the following type. Characterize which of the spaces from a given class support a semigroup of prescribed shape satisfying a given topological ergodic property. In particular, we characterize LBS-spaces (...

ε-weakly Chebyshev subspaces and quotient spaces