We work with very general Banach spaces of analytic functions in the disk or other domains which satisfy a minimum number of natural axioms. Among the preliminary results, we discuss some implications of the basic axioms and identify all functional Banach spaces in which every bounded analytic function is a pointwise multiplier. Next, we characterize (in various ways) the weighted composition operators among the bounded operators on such spaces, thus generalizing some well-known results on multiplication or composition operators. We also characterize the invertible weighted composition operators on the disk and on general Banach spaces of analytic functions on bounded domains under different sets of axioms whose connections we discuss by providing appropriate examples This generalizes and complements various recent results by Gunatillake, Bourdon, and Hyvärinen–Lindström–Nieminen–Saukko.

中文翻译：

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功能Banach空间中的加权合成算子：公理化方法

我们在磁盘或其他满足最少自然公理数量的域中使用非常通用的分析功能的Banach空间。在初步结果中，我们讨论了基本公理的某些含义，并确定了所有有功能的Banach空间，其中每个有界的解析函数都是点乘数。接下来，我们在这些空间上的有界算子中表征（以各种方式）加权合成算子，从而归纳了一些关于乘法或合成算子的众所周知的结果。我们还通过不同的公理集描述了磁盘上以及有界域上解析函数的一般解析函数的一般Banach空间上的可逆加权合成算子，我们将通过提供适当的例子对其进行讨论。