Journal of the Ramanujan Mathematical Society
Volume 40, Issue 3, September 2025 pp. 265–268.
On the numerical radius in
Hilbert C{*}-modules
Authors:
Biljana Vujošević
Author institution:University of Belgrade, Faculty of Mathematics, Studentski trg 16-18, Beograd, 11000, Serbia.
Summary:
In this paper we discuss the numerical radius in Hilbert modules
Ω(·), previously defined by A. Zamani [Math. Inequal.
Appl. 24, 4 (2021), 1017–1030]. Therein it is proved that
for a Hilbert module E over a C{*}-algebra {B} the
inequalities 1/2 ‖x‖ ≤ Ω(x) ≤ ‖x‖ hold for
all x ∈ E. In this paper we prove that there holds
Ω(x) = 1/2 ‖x‖ for all x ∈ E.
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