In this paper the author shows that a well known sufficient condition for strict cycliclty of a weighted shift on I_p is not a necessary condition for any p with 1 < p < ∞.
Wang, Y., & Sun, Q. (2007). A Note on ⊕-Cofinitely Supplemented Modules. International Journal of Mathematics and Mathematical Sciences, 2007(), 18-22. https://doi.org/10.1155/2007/10836
Hao, B. L. (1998). Applied Symbolic Dynamics. Chinese Journal of Physics, 36(6), 753-757. https://www.airitilibrary.com/Article/Detail?DocID=05779073-199812-201211010028-201211010028-753-757