Commutativity of the Arens product in lattice ordered algebras

Commutativity of the Arens product in lattice ordered algebras Let $${\text{A}}$$ be an Abelian Archimedean lattice ordered algebra. The order bidual $${A''}$$ furnished with the Arens product is again a lattice ordered algebra. We show that the order continuous order bidual $$(A')'_n$$ is Abelian. This solves an open problem and improves a result of Scheffold, who proved it for the case of normed lattice ordered algebras. The proof is based on the ‘up-down-up’ approximation of positive elements in the order continuous order bidual $$(A')'_n$$ by elements in the canonical image $${\widehat A}$$ of $$A$$ in $$(A')'_n$$ Components of positive elements in $${\widehat A}$$ are characterized and the result is applied to the Arens product of $$f$$ -and almost $$f$$ -algebras. Positivity Springer Journals

Commutativity of the Arens product in lattice ordered algebras

Positivity , Volume 3 (4) – Oct 22, 2004

Loading next page...
Kluwer Academic Publishers
Copyright © 1999 by Kluwer Academic Publishers
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial