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 ) 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
Published: Jul 6, 2013
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