Abstract. We first characterize those composition operators that are essentially normal on the weighted Bergman space $A^2_s(D)$ for any real $s>-1$, where induced symbols are automorphisms of the unit disk $D$. Using the same technique, we investigate automorphic composition operators on the Hardy space $H^2(B_N)$ and the weighted Bergman spaces $A^2_s(B_N)$ ($s>-1$). Furthermore, we give some composition operators induced by linear fractional self-maps of the unit ball $B_N$ that are not essentially normal.

DOI: 10.14232/actasm-014-060-x

AMS Subject Classification (1991): 47B33; 32A35, 32A36

Keyword(s): composition operator, essentially normal, automorphism, linear fractional maps

Received August 19, 2014, and in revised form October 19, 2014. (Registered under 60/2014.)