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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Erratum to: Complement of forms

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Publisher
Springer Basel
Copyright
Copyright © 2013 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-013-0250-8
Publisher site
See Article on Publisher Site

Abstract

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

Journal

PositivitySpringer Journals

Published: Jul 6, 2013

References

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