George Costakis, Antonios Manoussos
Published 2007-04-25, updated 2008-06-23Version 3
We provide a characterization of $J$-class and $J^{mix}$-class unilateral weighted shifts on $l^{\infty}(\mathbb{N})$ in terms of their weight sequences. In contrast to the previously mentioned result we show that a bilateral weighted shift on $l^{\infty}(\mathbb{Z})$ cannot be a $J$-class operator.
Comments: We correct some of the statements and the proofs
On distribution and almost convergence of bounded sequences
On the range of $\sum_{n=1}^\infty\pm c_n$
Szemeredi's theorem, frequent hypercyclicity and multiple recurrence
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