In this article we introduce a new class of Rolewicz-type operators in l_p, $1 le p < infty$. We exhibit a collection F having the cardinality of the continuum, consisting of operators of this type which are chaotic and remain so under almost all finite linear combinations, provided that the linear combination has sufficiently large norm. As a corollary to our main result we also obtain that there exists a countable collection of such operators whose all finite linear combinations are chaotic provided that they have sufficiently large norm.
Bongiorno, D., Darji, U., Di Piazza, L. (2015). Rolewicz-type chaotic operators. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 431(1), 518-528 [10.1016/j.jmaa.2015.05.073].
Rolewicz-type chaotic operators
BONGIORNO, Donatella
;DI PIAZZA, Luisa
2015-01-01
Abstract
In this article we introduce a new class of Rolewicz-type operators in l_p, $1 le p < infty$. We exhibit a collection F having the cardinality of the continuum, consisting of operators of this type which are chaotic and remain so under almost all finite linear combinations, provided that the linear combination has sufficiently large norm. As a corollary to our main result we also obtain that there exists a countable collection of such operators whose all finite linear combinations are chaotic provided that they have sufficiently large norm.
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