On the boundedness of multiplicative and positive functionals Academic Article uri icon

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abstract

  • AbstractLet A be a complex sequentially complete, locally convex (not necessarily commutative) topological algebra with the defining family {pα}αD of seminorms in which (*): for each sequence xn → 0 there exists xm ∈ {xn} such that xmk → 0 as k → ∞. Then each multiplicative linear functional on a Fréchet algebra satisfying the above condition (*) is Continuous.These results answer open questions (1) and (2) (Mem. Amer. Math. Soc. 11, 1953) in the affirmative for Fréchet algebras in which (*) holds. It is also shown that a positive linear functional on such algebras with identity and continuous involution is continuous, thus partially generalizing Shah's result (1959).

publication date

  • June 1976