Some further results on ideal summability of nets in ( $$\ell $$ ℓ ) groups

Some further results on ideal summability of nets in ( $$\ell $$ ℓ ) groups In this paper we continue in the line of recent investigation of order summability of nets using ideals by Boccuto et al. (Czechoslovak Math. J. 62(137):1073–1083 2012; J. Appl. Anal. 20(1), 2014) where they had introduced the notions of $$\mathcal {I}$$ I and $$\mathcal {I}^*$$ I ∗ order convergence, $$\mathcal {I}$$ I and $$\mathcal {I}^*$$ I ∗ divergence of nets and its further extensions, namely the notions of $$\mathcal {I}^{\mathcal {K}}$$ I K -order convergence and $$\mathcal {I}^{\mathcal {K}}$$ I K -divergence of nets in a $$(\ell )$$ ( ℓ ) -group and investigate the relation between $$\mathcal {I}$$ I and $$\mathcal {I}^{\mathcal {K}}$$ I K -concepts where a special class of ideals called $$\Lambda P(\mathcal {I},\mathcal {K})-$$ Λ P ( I , K ) - ideals plays very important role. We also introduce, for the first time, the notion of $$\mathcal {I}^{\mathcal {K}}$$ I K -order Cauchy condition and $$\mathcal {I}$$ I -order cluster points of nets in ( $$\ell $$ ℓ ) groups and examine some of its characterizations and its consequences. In particular the role of $$\mathcal {I}$$ I -order cluster points in making the above mentioned Cauchy nets convergent is studied. Positivity Springer Journals

Some further results on ideal summability of nets in ( $$\ell $$ ℓ ) groups

Loading next page...
Springer Basel
Copyright © 2014 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


  • On $$I$$ I -convergence of nets in locally solid Riesz spaces
    Das, P; Savas, E

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