An extension of the notion induced by Toeplitz and Hankel operators

Abstract

This paper introduces the notion of slant Toep-Hank operator L φ , with symbol φ in L ∞ (T), on the space L 2 (T), T being the unit circle. Along with a matrix characterization for an operator to be slant Toep-Hank , we characterize the symbols for the slant Toep-Hank operator to be compact and hyponormal. Some properties for the compression of slant Toep-Hank operators are also derived.