Algebraic Operator radius inequalities on C * -algebras

Let [Formula: see text] be a unital [Formula: see text]-algebra. In this paper, we establish several new inequalities involving the algebraic numerical radius and the algebraic Euclidean operator radius of elements in [Formula: see text]. We further introduce the algebraic [Formula: see text]-operator radius, [Formula: see text], for [Formula: see text]-tuples of elements in [Formula: see text], which extends the algebraic Euclidean operator radius. It is defined as [Formula: see text] where [Formula: see text] Our results generalize several known operator radius inequalities, and the corresponding inequalities for the algebraic Euclidean operator radius are recovered as special cases when [Formula: see text].