Abstract. In this paper, we discuss the conditions under which composition operators and weighted composition operators become quasi-$A(n)$ operators, quasi-$*$-$A(n)$ operators, $k$-quasi-$A(n)$ operators and $k$-quasi-$*$-$A(n)$ operators in terms of the Radon--Nikodym derivative $h_n$.

DOI: 10.14232/actasm-017-032-5

AMS Subject Classification (1991): 47B33, 47B20; 46C05

Keyword(s): composition operators, weighted composition operators, quasi-$A(n)$ operators, quasi-$*$-$A(n)$ operators, $k$-quasi-$A(n)$ operators and $k$-quasi-$*$-$A(n)$ operators

Received May 23, 2017, and in revised form November 27, 2017. (Registered under 32/2017.)