Infinite Toeplitz Matrices
Albrecht Böttcher, Sergei M. Grudsky · Hindustan Book Agency · 2000
Given a sequence \(\left\{ {{a_n}} \right\}_{n = - \infty }^\infty\) of complex numbers, a n ∈ C, when does the matrix $$A = \left( {\begin{array}{*{20}{c}} {{a_0}} & {{a_{ - 1}}} & {{a_{ - 2}}} & \cdots \\ {{a_1}} & {{a_0}} & {{a_{ - 1}}} & \cdots \\ {{a_2}} & {{a_1}} & {{a_0}} & \cdots \\ \cdots & \cdots & \cdots & \cdots \\ \end{array} } \right)$$ (1.1) induce a bounded operator on l2 ≔ l2(Z+), where Z+ is the set of nonnegative integers, Z+ ≔ {0,1,2,…}? The answer is classical result by Otto Toeplitz.