Operator Equations Inducing Some Generalizations of Slant Hankel Operators

An extension of slant Hankel operator, namely, the kth-order λ-slant Hankel operator on the Lebesgue space L2（T~n）, where T is the unit circle and n ≥ 1, a natural number, is described in terms of the solution of a system of operator equations, which is subsequently expressed in terms of the product of a slant Hankel operator and a unitary operator. The study is further lifted in Calkin algebra in terms of essentially kth-order λ-slant Hankel operators on L2（T~n）.