Complex symmetric weighted composition operators on H_gamma(D)

Generalized weighted composition operators on weighted Hardy spaces

“…Conversely, assume that ψ (m) (0), ϕ ′ (0) ∈ R and ϕ(0) = wϕ(0). Obviously, it is sufficient to verify that equation (19) holds. Since ϕ(0) = wϕ(0) and…”

“…In recent decades, complex symmetric composition operators and weighted composition operators acting on some Hilbert spaces of analytic functions have been studied considerably. See [3][4][5][6][7][8][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]28] for more results on complex symmetric operators.…”

Complex symmetry of multiplication and composition operators on A12(D)

“…Recall that the composition operator on the Classical Hardy space H 2 (D) and Bergman space A 2 (D) is bounded and the following theorem shows that any linear fractional map ψ on D to itself also induces a bounded composition operator on A 2 1 (D). Also, as mentioned in [12], a weighted composition operator is invariant if and only if it is bounded . Hence, composition operators on the Bergman space and the classical Hardy space are invariant.…”

“…Then equation (12) gives us that ψ(v) = b 0 + b 1 (q(v)/p(v)) and for b 2 = 3Φ(0), using equation ( 6) we get Φ(v) = b 2 p(v), for all v ∈ D. Proof. The proof follows from Theorem 3.9 and Theorem 3.10.…”

Complex symmetric weighted composition operators on Dirichlet spaces and Hardy spaces in the unit ball

“…Since all conjugation can be considered as a product of a J-symmetric unitary operator U and the conjugation J. Fatehi in [3] find all unitary weighted composition operators which are J-symmetric and consider complex symmetric weighted composition operators with special conjugation W ka,ϕa J on H 2 (D). Moreover, a criterion for complex symmetric structure of W ψ,ϕ on H γ (D) (with reproducing kernels K γ w = (1 − wz) −γ , where γ ∈ N) was discovered in [12]. In [19], Yuan and Zhou characterized the adjoint of linear fractional composition operators C ϕ acting on D(B N ).…”