Complex symmetric weighted composition operators on Hγ(D)

Complex symmetry of Toeplitz operators

“…for functions f ∈ H 2 . Such conjugations are introduced in [15] where complex symmetric weighted composition operators have been studied. Clearly, if u = µ and v = λz for some µ, λ ∈ T, then A u,v = µC λ .…”

“…The class of complex symmetric operators is very large and includes not only normal operators but also lots of nonnormal operators containing Hankel operators, truncated Toeplitz operators and Volterra integration operators. In order to obtain a better understanding for complex symmetric operators, a lot of effort are devoted to the study of complex symmetricity for several kinds of operators containing partial isometries [7], weighted shifts [20], triangular operators [19] and composition operators [11,12,15,16,18].…”

2-complex symmetric composition operators on $H^2$

“…The general study of complex symmetric operators was initiated by Garcia, Putinar and Wogen in [8][9][10][11]. See [6,7,12,13,[17][18][19][20][21] for more results on complex symmetric operators.…”

Normal complex symmetric weighted composition operators on the Hardy space

“…In [15], Lim and Khoi classified the weighted anti-linear conjugation A u,v into two cases C 1 and C 2 and presented the equivalent conditions of the C 1 −symmetric and C 2 −symmetric W ψ,ϕ on H γ (D). In [2], Bourdon and Narayan investigate the normality of W ψ,ϕ on H 2 (D) when ϕ has an interior fixed point or a Denjoy-Wolff point on D respectively.…”