Topological transitive sequence of cosine operators on Orlicz space

2018/09/17 by Ibrahim Akbarbaglu, Akbarbaglu, Ibrahim, Mohammad Reza Azimi +3
Mathematics · #46E30 (Primary) 22D05 (Secondary) #47A16 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:22D05 #msc:46E30 #msc:47A16

paper · pdf · doi:10.48550/arxiv.1809.06085

11 pages, Typos corrected, Title changed

arxiv created 2018/09/30 · arxiv updated 2018/10/02

Abstract

For a Young function ϕ and a locally compact second countable group G, let L^ϕ(G) denote the Orlicz space on G. In this article, we present a necessary and sufficient condition for the topological transitivity of a sequence of cosine operators \C_n\_n=1^∞:=\(1)/(2)(Tⁿ_g,w+Sⁿ_g,w)\_n=1^∞, defined on L^ϕ(G). We investigate the conditions for a sequence of cosine operators to be topological mixing. Moreover, we go on to prove the similar results for the direct sum of a sequence of the cosine operators. At the last, an example of a topological transitive sequence of cosine operators is given.

Related

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• Chaotic translations on weighted Orlicz spaces
• Dynamics of weighted translations on Orlicz spaces
• Dynamics of perturbations of the identity operator by multiples of the backward shift on l^∞(ℕ)
• Compact operators under Orlicz functions