Riemann曲面上的正常和拟正常复合算子

NORMAL AND QUASINORMAL COMPOSITION OPERATORS ON RIEMANN SURFACES

Riemann曲面M上的平方可测1-形式全体和解析1-形式全体均可构成Hilbert空间。本文讨论Riemann曲面上的解析映射导出的这类Hilbert空间上的复合算子,研究复合算子的正常性、拟正常性的诱导映射特征。特别地,当M有有限三角剖分时,证明了正常复合算子、拟正常复合算子、酉复合算子、等距复合算子和可逆复合算子等价。

The author considers composition operators on appropriate Hilbert spaced to Riamann surfaces. An important feature of Riemann surfaces is that locally they look like the complex plane. But functions on a Riemann surface do naturally form a Banach space. However, both measurable 1-forms and analytic 1-forms that are square integrable produce interesting Hilbert spaces. The purpose of this paper is to discuss the normality, the quasinormality, the unitarity and the invertibility of composition operators on these spaces.