Complex symmetric weighted composition operators on the Hardy space

Abstract

This paper provides a class of complex symmetric weighted composition operators on H 2 (D) to includes the unitary subclass, the Hermitian subclass and the normal subclass obtained by Bourdon and Noor. A characterization of algebraic weighted composition operator with degree no more than two is provided to illustrate that the weight function of a complex symmetric weighted composition operator is not necessarily linear fractional.2010 Mathematics Subject Classification. 47B33, 47B38.

Generalized weighted composition operators on weighted Hardy spaces

“…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.…”

$C$-normal weighted composition operators on $H^2$

“…Proof. Since W ψ,ϕ is normal, using Lemma 3 in [9], we have |b| = |c|. W ψ,ϕ is JW ξ p ,τ p -normal if and only if…”