Essentially generalized $λ$-slant Toeplitz operators

Abstract

We introduce the notion of an essentially generalized $λ$-slant Toeplitz operator on the Hilbert space $L^2$ for a general complex number $λ$, via the operator equation $λM_{z}X - XM_{z^{k}} = K$, $K$ being a compact operator on $L^2$ and $k(≥ 2)$ being an integer. We attempt to investigate some of the properties of this operator and also study its counterpart on $H^2$.