A new topology on $B^{\ast }$-algebras arising from the Arens products
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- by Edith A. McCharen
- Proc. Amer. Math. Soc. 37 (1973), 77-83
- DOI: https://doi.org/10.1090/S0002-9939-1973-0310638-1
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Abstract:
A locally convex topology $\mu$ is defined on a Banach algebra A. This topology arises naturally from considerations of the Arens products on the second conjugate space ${A^{ \ast \ast }}$ of A. The main result states that if A is a ${B^\ast }$-algebra on which the mapping $(a,b) \to ab$ is $\mu$-continuous for $\left \| a \right \| \leqq 1$, then the completion of A with respect to the uniformity generated by $\mu$ is linearly isomorphic to ${A^{ \ast \ast }}$. An example is included which shows that this continuity condition does not hold in general as announced by P. C. Shields.References
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 77-83
- MSC: Primary 46H05; Secondary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0310638-1
- MathSciNet review: 0310638