Complex symmetric composition operators on a Hilbert space of Dirichlet series

Abstract

On the Hilbert space of Dirichlet series with square summable coefficients, there are no non-normal complex symmetric composition operators induced by non-constant symbols. This is in sharp contrast with the phenomenon on the classical Hardy space over the unit disk.

3-Complex Symmetric and Complex Normal Weighted Composition Operators on the Weighted Bergman Spaces of the Half-Plane

“…At the beginning, research was mainly focused on the study of complex symmetric operators on abstract Hilbert spaces (see [3][4][5]). As research continued, experts and scholars began to consider some special complex symmetric operators (such as composition operators and weighted composition operators) on analytic function spaces (see [6][7][8][9][10][11][12][13][14][15]).…”

2-Complex Symmetric Composition Operators on H2

“…The study of complex symmetric operators was initiated by Garcia, Putinar, and Wogen in [1][2][3][4]. See [5][6][7][8][9][10][11][12][13][14] for more results on complex symmetric operators. Definition 3.…”

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.…”

“…Conversely, assume that ϕ(0) = wϕ(0). By a simple calculation, equation (26) holds. The proof is complete.…”