Complex symmetry of invertible composition operators

Complex symmetric composition operators induced by linear fractional maps

“…The first step is, of course, to determine the complex symmetric composition operators induced by automorphisms. Bourdon and Waleed Noor considered this problem in [2]. The next proposition is Proposition 2.1 in [2].…”

“…Bourdon and Waleed Noor considered this problem in [2]. The next proposition is Proposition 2.1 in [2]. Proposition 1.1.…”

“…Thanks to this proposition, we only need to investigate the elliptic automorphisms of the unit disk D. It turns out that things depend much on the orders of the automorphisms. Most of the cases are settled by the following proposition, which is one of the main results in [2].…”

Complex symmetric composition operators on H2

“…Due to a result of Garcia and Wogen [10], any automorphism of order 2 is complex symmetric. In [2], Bourdon and Noor found that other automorphisms cannot be complex symmetric except possibly for the unsolved case when ϕ is an elliptic automorphism of order 3. In [12], Noor found the exact conjugation needed for the involutive disk automorphisms to induce complex symmetric composition operators.…”

Complex symmetry & weighted composition operators on fock spaces

“…Aside from these investigations, several authors [1,5,6,19] took considerable effort to settle the automorphic and linear fractional symbols ϕ. The general problem is still challenging to the operator theory community, even in the case of composition operators C ϕ .…”