Excursions in Numerical Ranges
by
Pei Yuan Wu
Hwa-Long Gau
Vol. 9 No. 3 (2014) P.351~P.370
ABSTRACT
We survey some of our recent results on three topics in the study of numerical ranges,
namely, (1) Anderson’s condition for the numerical range of a finite matrix to equal a
circular disc, (2) Holbrook’s conjecture on the numerical radius inequality concerning the
product of two commuting operators, and (3) Williams and Crimmins’s structure theorem
on an operator when its numerical radius equals half of its norm.
KEYWORDS
Numerical range, numerical radius
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 15A60, 47A12
MILESTONES
Received: 2013-09-05
Revised : 2014-07-10
Accepted: 2014-07-10
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