On λ-k-skew Lie product involving commuting additive maps on prime ∗-algebras

Abstract

Let [Formula: see text] be an ∗-algebra and [Formula: see text]. For [Formula: see text], the product defined by [Formula: see text], where [Formula: see text] and [Formula: see text], is called [Formula: see text]-[Formula: see text]-skew Lie product of [Formula: see text] and [Formula: see text], where [Formula: see text]. This paper discusses some useful characteristics of [Formula: see text]-[Formula: see text]-skew Lie products on prime ∗-algebras. Moreover, we investigate the effects of an additive map [Formula: see text] on [Formula: see text] with a [Formula: see text]-[Formula: see text]-skew Lie product.