For a positive integer k ≥ 2, the kth-order slant weighted Toeplitz operatorThe paper derives relations among the symbols of two kth-order slant weighted Toeplitz operators so that their product is a kth-order slant weighted Toeplitz operator. We also discuss the compactness and the case for two kth-order slant weighted Toeplitz operators to commute essentially. Mathematics Subject Classification 47B37 · 47B35

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 .

The present paper introduces the class of weighted generalized composition operators of higher order defined on the weighted Hardy spaces. The study of bounded operators belonging to this class is undertaken and an attempt is made to describe their structural and spectral properties.

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