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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