ON QUASI *-BARRELLED SPACES
Keywords:quasi ∗-barrelled spaces, bornivorous ∗-barrel
In this paper, a new class of .ocally convex spaces, called quasi *- barrelled spaces is introduced. These spaces are characterized by : A locally convex space $E$ is Quasi *-barrelled if every bornivorous *-barrel in $E$ is a neighbourhood of $O$ in $E$. This class of spaces is a generalization of quasi-barrelled spaces and *-barrelled spaces (K.Anjaneyulu; Gayal : Jour. Math. Phy. Sci. Madras, 1984). Some properties of quasi *-barrelled spaces are sturued. Lastly one example each of
(i) a quasi *-barrelled space which is not quasi-barrelled.
(ii) a quasi *-barrelled space which is not *-barrelled.
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