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Algebras of frequently hypercyclic vectors
Author(s) -
Falcó Javier,
GrosseErdmann KarlG.
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900184
Subject(s) - mathematics , operator (biology) , multiplication (music) , multiplication operator , pure mathematics , product (mathematics) , operator algebra , crossed product , space (punctuation) , algebra over a field , banach space , hadamard product , hadamard transform , discrete mathematics , combinatorics , mathematical analysis , hilbert space , computer science , biochemistry , chemistry , geometry , repressor , transcription factor , gene , operating system
We show that the multiples of the backward shift operator on the spaces ℓp , 1 ≤ p < ∞ , or c 0 , when endowed with coordinatewise multiplication, do not possess frequently hypercyclic algebras. More generally, we characterize the existence of algebras of 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, F H C ( T ) is algebrable for a suitable product, and in some cases it is even strongly algebrable.