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Hankel matrix transforms and operators. (English) Zbl 1309.47028
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.

##### MSC:
 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 41A35 Approximation by operators (in particular, by integral operators)
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