Weak -convex algebras

Author:
Allan C. Cochran

Journal:
Proc. Amer. Math. Soc. **26** (1970), 73-77

MSC:
Primary 46.50

DOI:
https://doi.org/10.1090/S0002-9939-1970-0262830-X

MathSciNet review:
0262830

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Abstract: Necessary and sufficient conditions are given in terms of that a weak topology on an algebra be -convex. The main condition is that each element of contain a weakly closed subspace of finite codimension such that is bounded on all multiplicative translates of . For weak topologies, -convexity (which assumes only separate continuity of multiplication) is equivalent to joint continuity of multiplication.

**[1]**Richard Arens,*A generalization of normed rings*, Pacific J. Math.**2**(1952), 455–471. MR**0051445****[2]**A. C. Cochran, C. R. Williams and E. Keown,*On a class of topological algebras*, Pacific J. Math. (to appear).**[3]**Ernest A. Michael,*Locally multiplicatively-convex topological algebras*, Mem. Amer. Math. Soc.,**No. 11**(1952), 79. MR**0051444****[4]**Seth Warner,*Weak locally multiplicatively-convex algebras*, Pacific J. Math.**5**(1955), 1025–1032. MR**0076295****[5]**Seth Warner,*Inductive limits of normed algebras*, Trans. Amer. Math. Soc.**82**(1956), 190–216. MR**0079226**, https://doi.org/10.1090/S0002-9947-1956-0079226-3**[6]**W. H. Summers,*A representation theorem for biequicontinuous completed tensor products of weighted spaces*, Trans. Amer. Math. Soc.**146**(1969), 121–131. MR**0251521**, https://doi.org/10.1090/S0002-9947-1969-0251521-3

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DOI:
https://doi.org/10.1090/S0002-9939-1970-0262830-X

Keywords:
-convex algebra,
locally -convex algebra,
weak topology,
topological algebra

Article copyright:
© Copyright 1970
American Mathematical Society