On the Theory of L p (L q )-Banach Lattices

On the Theory of L p (L q )-Banach Lattices Given 1≤ p,q < ∞, let BL p L q be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some L p (L q )-Banach lattice. We show that the range of a positive contractive projection on any BL p L q -Banach lattice is itself in BL p L q . It is a consequence of this theorem and previous results that BL p L q is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BL p L q -Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for BL p L q . We also consider the class of all sublattices of L p (L q )-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of L p -Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

On the Theory of L p (L q )-Banach Lattices

Loading next page...
Copyright © 2007 by Birkhäuser Verlag, Basel
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