arXiv subjects
Publications and source records attributed to Xingxing Yao.
This paper is devoted to an in-depth study of the minimal commutant property for composition operators acting on Hilbert spaces of holomorphic functions in several complex variables, such as the Fock space on $\mathbb{C}^d$, the Hardy space on the Euclidean ball, and the Hardy space on the unit polydisc.
Let $φ$ be a holomorphic map which is a symbol of a bounded composition operator $C_φ$ acting on the Hardy-Hilbert space of Dirichlet series. We find a Königs map for $φ$. We then deduce several applications on $C_φ$ (e.g. on its spectrum, on its dynamical properties). In particular, we study for a large class of symbols $φ$ if the associated composition operator has a minimal commutant.
The aim of this paper is to study when two composition operators on the Hilbert space of Dirichlet series with square summable coefficients belong to the same component or when their difference is compact. As a corollary we show that if a linear combination of composition operators with polynomial symbols of degree at most 2 is compact, then each composition operator is compact.