Infinite Toeplitz Matrices

Given a sequence \( \left\{ {{a_n}} \right\}_{{n = - \infty }}^{\infty } \) of complex numbers, an ∈ C, when does the matrix $$ A = \left( {\begin{array}{*{20}{c}} {{a_0}} & {{a_{{ - 1}}}} & {{a_{{ - 2}}}} & {...} \\ {{a_1}} & {{a_0}} & {{a_{{ - 1}}}} & {...} \\ {{a_2}} & {{a_1}} & {{a_0}} & {...} \\ {...} & {...} & {...} & {...} \\ \end{array} } \right) $$ (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.