Tính compact của toán tử tuyến tính và đạo hàm của nó | Ngô Quốc Anh

January 7, 2008

Tính compact của toán tử tuyến tính và đạo hàm của nó

Filed under: Các Bài Tập Nhỏ, Linh Tinh — Ngô Quốc Anh @ 20:58

Let $G$ be an open set in Banach space $X$ . Assume that $G \to X$ is a compact operator and $x_0 \in G$ . If $f'(x_0)$ exists, then $f'(x_0)$ is also a compact operator.

$\displaystyle \boxed{ f : G \to X \text{ is compact}} \xrightarrow{{f'\left( {x_0 } \right)\text{ exists}}} \boxed{f'(x_0) : X \to X \text{ is compact}}$ .

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