$J$-class weighted translations on locally compact groups
M. R. Azimi, I. Akbarbaglu, A. R. Imanzadeh Fard

TL;DR
This paper characterizes when weighted translation operators on locally compact groups exhibit $J$-class behavior, exploring the boundary with hypercyclicity and providing examples where $J$-class occurs without hypercyclicity.
Contribution
It establishes necessary and sufficient conditions for weighted translations to be $J$-class on $L^p$-spaces and distinguishes $J$-class from hypercyclic operators in this setting.
Findings
Identifies conditions for $J$-class weighted translations on locally compact groups.
Shows $J$-class behavior can occur without hypercyclicity.
Provides examples illustrating $J$-class but not hypercyclic operators.
Abstract
A bounded linear operator on a Banach space (not necessarily separable) is said to be -class operator whenever the extended limit set, say equals for some vector . Practically, the extended limit sets localize the dynamical behavior of operators. In this paper, using the extended limit sets we will examine the necessary and sufficient conditions for the weighted translation to be -class on a locally compact group , within the setting of -spaces for . Precisely, we delineate the boundary between -class and hypercyclic behavior for weighted translations. Then, we will show that for torsion elements in locally compact groups, unlike the case of non-dense orbits of weighted translations, we have . Finally, we will provide some examples on which the weighted translation $…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Operator Algebra Research · Functional Equations Stability Results
