Erratum to: Complement of forms

Erratum to: Complement of forms Positivity (2013) 17:941–943 DOI 10.1007/s11117-013-0250-8 Positivity ERRATUM Zoltán Sebestyén · Tamás Titkos Published online: 6 July 2013 © Springer Basel 2013 Erratum to: Positivity (2013) 17:1–15 DOI 10.1007/s11117-011-0138-4 The original publication of this paper contained an error in Lemma 2(g). The statement (which is used later in Theorem 6, Lemma 12, and Theorem 11) is false in general. We will show that D t ↑ D t whenever w ↑ w and w is dominated by t. Since w w k this condition is satisfied in Theorem 6, Lemma 12, and Theorem 11, the results remain true (with the same proof). The first part of the following theorem is the reformulation of (Proposition 5.1 in [1]) for nonnegative sesquilinear forms, the second part is an easy consequence. This is the correct version of Lemma 2(g). Theorem 1 Let t, w, and w (k ∈ N) be nonnegative sesquilinear forms on the complex linear space D. Assume further that w ↑ w, and w ≤ αt for some α> 0. Then sup(w : t) = sup w : t = w : t and sup D t = D t = D t. k k w sup w w k Positivity Springer Journals

Erratum to: Complement of forms

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