Functional representation of topological algebras

The space of bounded sequences with the mixed topology

“…Also in view of VIII, E is a topological algebra in the sense of [9]. Combining Theorem 4.6 of [9] and IX above we get the required result. REMARK 6.…”

“…REMARK 5. We note that m-barrelledness of some topology compatible with duality is sufficient in [8], Lemma 3.1 (or [9], Cor. 6.3) and even this condition is not necessary as shown by II and VII.…”

Representation of Locally Convex Algebras

“…Moreover [9], 0 is open lito (7(M) with tite compact open topology ib anO only ib every equicontinuous subset fi ob tite topological dual E' ob E is contauned in a-rnultiple ob the closed convex huil of sorne equicontununus subset of M. In particular, E must be m-convex. Now, let X be a Hausdorff completely regular spa-ce.…”

“…Titis work consists obthree indepenOant sections. In [9], conditions are given under witich E is embedded aigebraicaily (anO topologica-lIy) in sorne (7(X) with tite compa-ct open topology or a-weaker topology. A.C. Cocitran sitows iii [4] titat every semisimple uniformly A-convex algebra E can be embedded continuously, via tite Gelba-nd ma-p…”

On the Ideal Structure of Algebras of Star-Algebra Valued Functions

“…We shall say that (A, T(£P)) is a star algebra, if there is an involution x y-y x*, x £ A, in A such that px(xx*) = Px(x)2, x £ A, X £ A. The properties of star algebras can be found for example in [4], [7], [15], and [16]. See also [2].…”