An Extension of Amir-Lindenstrauss Theorem

Qiu Jing Hui

Abstract: In this paper we give an extension of Amir-Lindenstrauss Theorem on weak* sequential compactness as follows: if a locally convex space $X$ has a sequence $K_1 \subset K_2 \subset K_3 \subset\ldots$ of relatively weakly countably compact sets such that $\SPAN(\bigcup^{\infty}_{n=1}K_n)$ is dense in $X$, then each weak* compact absolutely convex subset of $X'$ is weak* sequentially compact. Using the extension we obtain an improvement of Kalton's closed graph theorem.

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