Abstract A conjecture posed by MacDonald and Rosenthal states the composition operator C φ acting on the Newton space N 2 ( P ) induced by φ ( z ) = m z + m − 1 2 is bounded, where m ∈ ( 0 , 1 ) . Our first result is proving that the aforementioned conjecture holds. We investigate complex symmetry of composition operators acting on the Newton space, which is different from that on the Hardy space. In addition, normality and co-isometry of composition operators are studied. Finally, we consider complex symmetric weighted composition operators.

中文翻译：

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牛顿空间上的复对称复合算子

摘要 MacDonald 和Rosenthal 提出的猜想陈述了作用于由φ ( z ) = mz + m − 1 2 引起的牛顿空间N 2 ( P ) 的合成算子C φ 是有界的，其中m ∈ ( 0 , 1 ) 。我们的第一个结果是证明上述猜想成立。我们研究了作用在牛顿空间上的复合算子的复杂对称性，这与哈代空间上的不同。此外，还研究了合成算子的正态性和共等距。最后，我们考虑复杂的对称加权组合算子。