On the Orlicz function estimations of the $a$-Davis--Wielandt radius in $C^{\ast }$-algebra

We present a systematic study of $a$-Davis–Wielandt radius estimates for elements in a unital $C^{\ast }$-algebra through an Orlicz function approach. We derive novel bounds for the algebraic $a$-Davis–Wielandt radius and further obtain estimates for the classical algebraic Davis–Wielandt radius via polar decomposition and the Moore–Penrose inverse. The results obtained in this work extend, generalize, and unify a variety of established inequalities in the literature as special cases.