Complex Symmetric Composition Operators on the Hardy Space of the Unit Ball

Abstract

In this paper, we introduce a new conjugation induced by a sequence of symmetric unitary n × n matrices on ℂⁿ. And we completely characterize the complex symmetric composition operator C_ϕ on the Hardy space of the unit ball with respect to the conjugation mentioned above. Furthermore, we propose an interesting open question under the background of this problem: whether every square complex matrix is symmetrically unitarily equivalent to its transpose (SUET).

Keywords

Complex symmetry / composition operator / Hardy space / unit ball

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Peking University