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引用次数: 13
摘要
形式为C h f = f°h的函数空间上的算子，其中h是一个固定映射，称为带符号h的复合算子。我们研究了作用于右半平面上的Hilbert Hardy空间上的这类算子，并描述了它们可逆、Fredholm、酉和厄米的情形。我们用inner和Möbius符号分别确定普通复合运算符。在选定的情况下，我们计算它们的光谱、基本光谱和数值范围。
Invertible and normal composition operators on the Hilbert Hardy space of a half–plane
Abstract Operators on function spaces of form Cɸf = f ∘ ɸ, where ɸ is a fixed map are called composition operators with symbol ɸ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra, essential spectra, and numerical ranges.
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