Defining operator

for a sequence $x=\{x_p\}$

An operator $M$ in a space of sequences having the form

$$(Mx)_p=\sum_{-l}^{+l}m_jx_{p-j};$$

$$m_j=\overline{m_{-j}},\quad\sum_{-l}^{+l}m_j\lambda^j\leq0,\quad|\lambda|=1;$$

converting the sequence $x$ to some positive sequence.