COMMUTATIVITY OF WEIGHTED SLANT HANKEL OPERATORS

Abstract

For a positive integer k 2, the kth-order weighted slant Hankel operator D k; on L2( ) with 2 L1( ) is de ned as D k; = J WkM , where J is the re ection operator given by J en = e􀀀n for each n 2 Z and Wk is given by Wken(z) = m km em(z) if n = km;m 2 Z and Wken(z) = 0 if n 6= km. The paper discusses the product and commutativity of kth-order weighted slant Hankel operators of di erent order. Compactness and essential commutativity of these operators are also addressed and it is obtained that the commutativity of these operators coincides with the essential commutativity.