Higher order complex symmetric operators and some of their related classes of operators

This paper investigates a novel family of complex symmetric operators, drawing parallels to the well-established (n, m)-normal operators (Alzuraiqi and Patel, in Gen Math Notes 1(2):61–73, 2010; Chō and Na \(\breve{c}\) $\breve{c}$ tovska in Filomat 32(14):5063–5069, 2018; Chō and Lee in Filomat 32(15):5441–5451, 2018; Jibril in J Sci Eng 33(2A):247-251, 2008; Mecheri in Oper Matrices 15(2):615-626, 2021) and k-quasi-(n, m)-normal operators (Ahmed et al. in Hacet J Math Stat 5(2):326–341, 2021). Through this exploration, we aim to uncover new properties and relationships within these classes, contributing to the broader understanding of operator theory.