Abstract
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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This work was supported by an N.R.C. Grant.
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Husain, T., Warsi, S.A. Positive functionals on BP*-algebras. Period Math Hung 8, 15–28 (1977). https://doi.org/10.1007/BF02018042
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DOI: https://doi.org/10.1007/BF02018042