PORTUGALIAE MATHEMATICA Vol. 52, No. 1, pp. 4147 (1995) 

An Extension of AmirLindenstrauss TheoremQiu Jing HuiDepartment of Mathematics, Suzhou University,Suzhou, Jiangsu  PEOPLE'S REPUBLIC OF CHINA Abstract: In this paper we give an extension of AmirLindenstrauss 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. Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1995 Sociedade Portuguesa de Matemática
