Chaotic Banach algebras

Research output: Contribution to journalArticlepeer-review

97 Downloads (Pure)

Abstract

We construct an infinite dimensional non-unital Banach algebra $A$ and $a\in A$ such that the sets $\{za^n:z\in\C,\ n\in\N\}$ and $\{({\bf 1}+a)^na:n\in\N\}$ are both dense in $A$, where $\bf 1$ is the unity in the unitalization $A^{\#}=A\oplus \spann\{{\bf 1}\}$ of $A$. As a byproduct, we get a hypercyclic operator $T$ on a Banach space such that $T\oplus T$ is non-cyclic and $\sigma(T)=\{1\}$.
Original languageEnglish
JournalJournal of Functional Analysis
Publication statusAccepted - 2013

Fingerprint

Dive into the research topics of 'Chaotic Banach algebras'. Together they form a unique fingerprint.

Cite this