Positivity (2013) 17:941–943
Erratum to: Complement of forms
Zoltán Sebestyén · Tamás Titko s
Published online: 6 July 2013
© Springer Basel 2013
Erratum to: Positivity (2013) 17:1–15
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
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.
: t) =
: t = w : t and sup
t = D
t = D
Proof Since w
: t ≤ w : t for all k ∈ N, the supremum (denoted by s)
The online version of the original article can be found under doi:10.1007/s11117-011-0138-4.
Z. Sebestyén · T. Titkos (
Department of Applied Analysis and Computational Mathematics,
Eötvös Loránd University, Pázmány Péter sétány 1/c., Budapest 1117, Hungary