谱映射定理
The Spectral Mapping Theorem
摘要：
本文给出了实谱巴拿赫空间上线性算子Helffer-Sjöstrand谓词演算的谱映射定理的直接非抽象证明，从而给出了希尔伯特空间上自伴算子的谱映射定理的一个新的非抽象直接证明.我们的论述在精神上更接近于戴维斯给出的谓词演算存在性的明确构造证明。本文应用Seeley的一个扩张定理导出了半有界算子的一个谓词演算。
英文摘要：
We give a direct non-abstract proof of the Spectral Mapping Theorem for the Helffer-Sjöstrand functional calculus for linear operators on Banach spaces with real spectra and consequently give a new non-abstract direct proof for the Spectral Mapping Theorem for self-adjoint operators on Hilbert spaces. Our exposition is closer in spirit to the proof by explicit construction of the existence of the Functional Calculus given by Davies. We apply an extension theorem of Seeley to derive a functional calculus for semi-bounded operators.
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