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Weighted composition operators on Korenblum type spaces of analytic functions
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas ( IF 1.8 ) Pub Date : 2020-09-05 , DOI: 10.1007/s13398-020-00924-1
Esther Gómez-Orts

We investigate the continuity, compactness and invertibility of weighted composition operators $$W_{\psi ,\varphi }{:}\, f \rightarrow \psi (f \circ \varphi )$$ when they act on the classical Korenblum space $$A^{-\infty }$$ and other related Frechet or (LB)-spaces of analytic functions on the open unit disc which are defined as intersections or unions of weighted Banach spaces with sup-norms. Some results about the spectrum of these operators are presented in case the self-map $$\varphi $$ has a fixed point in the unit disc. A precise description of the spectrum is obtained in this case when the operator acts on the Korenblum space.

中文翻译:

解析函数的 Korenblum 类型空间上的加权复合算子

我们研究了加权合成算子 $$W_{\psi ,\varphi }{:}\, f \rightarrow \psi (f \circ \varphi )$$ 作用于经典 Korenblum 空间 $$ 的连续性、紧凑性和可逆性$A^{-\infty }$$ 和其他相关的 Frechet 或 (LB)-开放单位圆盘上的解析函数空间,它们被定义为加权 Banach 空间与 sup-norms 的交集或并集。如果自映射 $$\varphi $$ 在单位盘中有一个不动点,则给出了关于这些算子的频谱的一些结果。在这种情况下,当算子作用于 Korenblum 空间时,可以获得频谱的精确描述。
更新日期:2020-09-05
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