0000000000174354

AUTHOR

Karl-g. Grosse-erdmann

showing 2 related works from this author

Algebras of frequently hypercyclic vectors

2019

We show that the multiples of the backward shift operator on the spaces $\ell_{p}$, $1\leq p<\infty$, or $c_{0}$, when endowed with coordinatewise multiplication, do not possess frequently hypercyclic algebras. More generally, we characterize the existence of algebras of $\mathcal{A}$-hypercyclic vectors for these operators. We also show that the differentiation operator on the space of entire functions, when endowed with the Hadamard product, does not possess frequently hypercyclic algebras. On the other hand, we show that for any frequently hypercyclic operator $T$ on any Banach space, $FHC(T)$ is algebrable for a suitable product, and in some cases it is even strongly algebrable.

Mathematics::Functional AnalysisPure mathematicsGeneral MathematicsEntire function010102 general mathematicsBanach spaceDynamical Systems (math.DS)Shift operatorSpace (mathematics)01 natural sciences010101 applied mathematicsStatistics::Machine LearningOperator (computer programming)Product (mathematics)Banach algebraFOS: MathematicsHadamard productMathematics - Dynamical Systems0101 mathematics47A16MathematicsMathematische Nachrichten
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Algebrability of the set of hypercyclic vectors for backward shift operators

2020

Abstract We study the existence of algebras of hypercyclic vectors for weighted backward shifts on Frechet sequence spaces that are algebras when endowed with coordinatewise multiplication or with the Cauchy product. As a particular case, we obtain that the sets of hypercyclic vectors for Rolewicz's and MacLane's operators are algebrable.

Set (abstract data type)Mathematics::Functional AnalysisPure mathematicsSequenceGeneral Mathematics010102 general mathematics0103 physical sciencesMultiplication010307 mathematical physics0101 mathematics01 natural sciencesCauchy productMathematicsAdvances in Mathematics
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