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

Abstract:

      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 E^p(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.