Existence of hypercyclic polynomials on complex Fréchet spaces
نویسندگان
چکیده
منابع مشابه
Existence and Nonexistence of Hypercyclic Semigroups
In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional Banach space that is very different from—and considerably shorter than—the one recently given by Bermúdez, Bonilla and Martinón. We also show the existence of a strongly dense family of topologically mixing operators on every separable infinite...
متن کاملExistence Results of best Proximity Pairs for a Certain Class of Noncyclic Mappings in Nonreflexive Banach Spaces Polynomials
Introduction Let be a nonempty subset of a normed linear space . A self-mapping is said to be nonexpansive provided that for all . In 1965, Browder showed that every nonexpansive self-mapping defined on a nonempty, bounded, closed and convex subset of a uniformly convex Banach space , has a fixed point. In the same year, Kirk generalized this existence result by using a geometric notion of ...
متن کاملBernstein's Lethargy Theorem in Fréchet spaces
In this paper we consider Bernstein’s Lethargy Theorem (BLT) in the context of Fréchet spaces. Let X be an infinite-dimensional Fréchet space and let V = {Vn} be a nested sequence of subspaces of X such that Vn ⊆ Vn+1 for any n ∈ N and X = ⋃∞ n=1 Vn. Let en be a decreasing sequence of positive numbers tending to 0. Under an additional natural condition on sup{dist(x, Vn)}, we prove that there e...
متن کاملSeries expansions in Fréchet spaces and their duals, construction of Fréchet frames
Frames for Fréchet spaces XF with respect to Fréchet sequence spaces ΘF are studied and conditions, implying series expansions in XF and X ∗ F , are determined. If {gi}i=1 is a Θ0-frame for X0, we construct a sequence {Xs}s∈N0 , Xs ⊂ Xs−1, s ∈ N, for given ΘF , respectively a sequence {Θs}s∈N0 , Θs ⊂ Θs−1, s∈N, for given XF , so that {gi}i=1 is a pre-F -frame (or F -frame) for XF with respect t...
متن کاملHypercyclic Behaviour of Operators in a Hypercyclic C0-Semigroup
Let {Tt}t≥0 be a hypercyclic strongly continuous semigroup of operators. Then each Tt (t > 0) is hypercyclic as a single operator, and it shares the set of hypercyclic vectors with the semigroup. This answers in the affirmative a natural question concerning hypercyclic C0-semigroups. The analogous result for frequent hypercyclicity is also obtained.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2009
ISSN: 0166-8641
DOI: 10.1016/j.topol.2009.02.010