Numerical ranges of products of two positive contractions

Hwa Long Gau, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Let A and B be positive contractions on a Hilbert space. It was known before that the numerical range W(AB) of their product is contained in the rectangular region [−1/8,1]×[−1/4,1/4]. In this paper, we determine exactly when W(AB) touches on its four sides. This follows from the more general information on a containing region of W(AB) and on when they share a common tangent line. We also give an example of A and B on three-dimensional space for which W(AB) is not symmetric with respect to the x-axis.

Original languageEnglish
Pages (from-to)939-946
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - 15 Nov 2017


  • Numerical range
  • Positive contraction


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