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  • 标题:Strictly barrelled disks in inductive limits of quasi-(LB)-spaces
  • 本地全文:下载
  • 作者:Carlos Bosch ; Thomas E. Gilsdorf
  • 期刊名称:International Journal of Mathematics and Mathematical Sciences
  • 印刷版ISSN:0161-1712
  • 电子版ISSN:1687-0425
  • 出版年度:1996
  • 卷号:19
  • 期号:4
  • 页码:727-732
  • DOI:10.1155/S0161171296001007
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    A strictly barrelled disk B in a Hausdorff locally convex space E is a disk such that the linear span of B with the topology of the Minkowski functional of B is a strictly barrelled space. Valdivia's closed graph theorems are used to show that closed strictly barrelled disk in a quasi- ( LB ) -space is bounded. It is shown that a locally strictly barrelled quasi- ( LB ) -space is locally complete. Also, we show that a regular inductive limit of quasi- ( LB ) -spaces is locally complete if and only if each closed bounded disk is a strictly barrelled disk in one of the constituents.

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