Retakh条件(M0)与弱(序列式)紧正则性

本文研究了弱(序列式)紧正则诱导极限与凸弱(序列式)紧正则诱导极限.满足Retakh条件(Mo)的(LF)-空间必为凸弱(序列式)紧正则的,但未必为弱(序列式)紧正则的.对于弱序列式完备Frechet空间的可数诱导极限,Retakh条件(Mo)蕴涵弱(序列式)紧正则性.特别地,对于Kothe(LF)-序列空间Ep(1≤p<∞),Retakh条件(Mo)等价于弱(序列式)紧正则性.对于这类空间,利用Vogt的有关结论,给出了弱(序列式)紧正则性的特征.

Retakh's Conditions (M0) and Weakly (Sequentially) Compact Regularity

Weakly (seqnentially) compactly regnlar inductive limits and convex weakly(sequentially) compactly regular inductive limits are investigated. (LF)-spaces satisfyingRetakh's condition (M0) are convex weakly (sequentially) compactly regular but neednot be weakly (sequentially) compactly regular. For conntable inductive limits of weaklysequentially complete Frechhet spaces, Retakh's condition (M0) implies weakly (sequen-tially) compact regularity. Particularly for Kothe (LF)-sequence spaces Ep(1 ≤ p ＜ x),Retakh's condition (M0) is equivalent to weakly (sequentially) compact regularity. Forthose spaces, the characterizations of weakly (seqnentially) compact regularity are givenby using the related results of Vogt.