Abstract :
An inductive limit E, t.sind En, tn.is regular if and only if it satisfies the
weak property Y0.; i.e., each weakly unconditionally Cauchy series in E, t. is
contained and is a weakly unconditionally Cauchy series in some En, tn.. In
particular, an LF.-space E, t.sind En, tn.is regular if and only if every weakly
unconditionally Cauchy series kxk is a C-series; i.e., for any scalar sequence
j k.gc0 , the series kjkxk is convergent. Furthermore, for inductive limits of
Fr´echet spaces containing no copy of c0 , a number of characteristic conditions of
regularity are given
Keywords :
inductive limit , LF.-space , Regularity , weak property Y0. , C-series.
