Sequential completeness of LF-spaces

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Sequential completeness of LF-spaces. (English). Czechoslovak Mathematical Journal, vol. 51 (2001), issue 1, pp. 181-183

MSC: 46A13, 46A30 | MR 1814643 | Zbl 1079.46502

Keywords:
LB- and LF-space; regularity and sequential completeness of locally convex inductive limits

Summary:
Any LF-space is sequentially complete iff it is regular.

References:

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[2] J. Kučera and K. McKennon: Quasi-incomplete regular LB-space. Internat. J. Math. 16 (1993), 675–678. DOI 10.1155/S0161171293000845 | MR 1234812

[3] B. M. Makarov: Pathological properties of inductive limits of Banach spaces. Uspekhi Mat. Nauk 18 (1963), 171–178. MR 0152867

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[5] M. de Wilde: Closed graph theorems and webbed spaces. Pitman, London, 1978. Zbl 0373.46007

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