Let $(X,T)$ be a linear dynamical system, where $X$ is a Banach space and $T:X \to X$ is a bounded linear operator. This paper obtains that $(X,T)$ is sensitive (Li-Yorke sensitive, mean sensitive, syndetically mean sensitive, respectively) if and only if $(X,T)$ is Banach mean sensitive (Banach mean Li-Yorke sensitive, thickly multi-mean sensitive, thickly syndetically mean sensitive, respectively). Several examples are provided to distinguish between different notions of mean sensitivity, syndetic mean sensitivity and mean Li-Yorke sensitivity.
Quanquan YAO
,
Peiyong ZHU
. MEAN SENSITIVITY AND BANACH MEAN SENSITIVITY FOR LINEAR OPERATORS[J]. Acta mathematica scientia, Series B, 2024
, 44(4)
: 1200
-1228
.
DOI: 10.1007/s10473-024-0402-x
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