On the Orlicz function estimations of the $a$-Davis--Wielandt radius in $C^*$-algebra

RESUMO

We present a systematic study of $a$-Davis--Wielandt radius estimates for elements in a unital $C^*$-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.