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 λMzX − 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 .

Essentially generalized lambda-slant Hankel operators

“…Throughout the paper, k is assumed to be an integer greater than or equal to 2. We begin with the following definitions, the detailed study of which can be seen in [3,6]. Definition 2.2.…”

Toeplitz and weighted Toeplitz operators on weighted sequence spaces

“…The study of Toeplitz operators becomes more demanding with the inception of the notion of slant Toeplitz operators by Ho [13] in 1996, which has widely appeared in connection with the wavelet theory, having the property that their matrices with respect to the standard orthonormal basis could be obtained by eliminating every alternate row of the matrices of the corresponding Toeplitz operators. The study in this direction is enhanced with the introduction of various new classes of operators over various function spaces, like, k th -order slant Toeplitz operators, essentially slant Toeplitz operators, λ-Toeplitz and essentially λ-Toeplitz operators, λ ∈ C, the set of all complex numbers (see the references [[1]- [7], [10]- [12]] and the references therein). Around the year 1966, the notion of weighted sequence spaces was brought forth by R.L.…”