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Article

Moradi, Abbas ; Hedayatian, Karim ; Khani Robati, Bahram ; Ansari, Mohammad
Non supercyclic subsets of linear isometries on Banach spaces of analytic functions. (English). Czechoslovak Mathematical Journal, vol. 65 (2015), issue 2, pp. 389-397
MSC: 47A16, 47B33, 47B38 | MR 3360435 | Zbl 06486955 | DOI: 10.1007/s10587-015-0184-3
Keywords:
supercyclicity; hypercyclic operator; semigroup; isometry
Summary:
Let $X$ be a Banach space of analytic functions on the open unit disk and $\Gamma $ a subset of linear isometries on $X$. Sufficient conditions are given for non-supercyclicity of $\Gamma $. In particular, we show that the semigroup of linear isometries on the spaces $S^p$ ($p>1$), the little Bloch space, and the group of surjective linear isometries on the big Bloch space are not supercyclic. Also, we observe that the groups of all surjective linear isometries on the Hardy space $H^p$ or the Bergman space $L^{p}_{a}$ ($1<p<\infty $, $p\neq 2$) are not supercyclic.
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