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  • Author or Editor: T. Husain x
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To investigate the continuity of positive functionals on certain topological*-algebras, we consider general locally convex and non-locally convex topological*-algebras which need not have identity or continuity of involution. We generalize a number of known results.

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Authors: T. Husain and S. A. Warsi

A new class of locally convex algebras, called BP*-algebras, is introduced. It is shown that this class properly includes MQ*-algebras which were introduced and studied by the first author andR. Rigelhof [10]. Among other results, it is proved that each positive functional on a BP*-algebraA is admissible but not necessarily continuous as shown by an example. However, ifA, in addition, is either (i) a Q-algebra, or (ii) has an identity and is barrelled, or (iii)A is endowed with the inductive limit topology, then each positive functional onA is continuous.

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