Hankel matrix transforms and operators (Q367116)

The article under review concerns Hankel matrices and Hankel operators. Reviewer's remark: The paper contains errors. In particular, the paper contains the following result: Theorem 3.1. A Hankel matrix is regular if and only if (i) \(\lim_{n\to\infty}h_{n+k}=0\). (ii) \(\lim_{n\to\infty}\sum_{k=1}^\infty h_{n+k}=1\). (iii) \(\sup_n\sum_{k=1}^\infty|h_{n+k}|\leq M\). Condition (i) is very strange. Clearly, \( \lim_{n\to\infty}h_{n+k}=\lim_{n\to\infty}h_n. \) Condition (iii) does not make any sense. If the series converges, then \(\lim_{n\to\infty}\sum_{k=1}^\infty h_{n+k}=0\). Condition (iii) is also strange. Clearly, the supremum in question involves a non increasing sequence.