Orthogonality in $$\ell _p$$ -spaces and its bearing on ordered Banach spaces

Orthogonality in $$\ell _p$$ -spaces and its bearing on ordered Banach spaces We introduce a notion of $$p$$ -orthogonality in a general Banach space for $$1 \le p \le \infty $$ . We use this concept to characterize $$\ell _p$$ -spaces among Banach spaces and also among complete order smooth $$p$$ -normed spaces as (ordered) Banach spaces with a total $$p$$ -orthonormal set (in the positive cone). We further introduce a notion of $$p$$ -orthogonal decomposition in order smooth $$p$$ -normed spaces. We prove that if the $$\infty $$ -orthogonal decomposition holds in an order smooth $$\infty $$ -normed space, then the $$1$$ -orthogonal decomposition holds in the dual space. We also give an example to show that the above said decomposition may not be unique. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Orthogonality in $$\ell _p$$ -spaces and its bearing on ordered Banach spaces

Positivity , Volume 18 (2) – May 16, 2013

Loading next page...
Springer Basel
Copyright © 2013 by Springer 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