Product of operators and numerical range

Mao Ting Chien, Hwa Long Gau, Chi Kwong Li, Ming Cheng Tsai, Kuo Zhong Wang

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We show that a bounded linear operator (Formula presented.) is a multiple of a unitary operator if and only if (Formula presented.) and (Formula presented.) always have the same numerical radius or the same numerical range for all (rank one) (Formula presented.). More generally, for any bounded linear operators (Formula presented.) , we show that (Formula presented.) and (Formula presented.) always have the same numerical radius (resp., the same numerical range) for all (rank one) (Formula presented.) if and only if (Formula presented.) (resp., (Formula presented.)) is a multiple of a unitary operator for some (Formula presented.). We extend the result to other types of generalized numerical ranges including the (Formula presented.) -numerical range and the higher rank numerical range.

Original languageEnglish
Pages (from-to)58-67
Number of pages10
JournalLinear and Multilinear Algebra
Volume64
Issue number1
DOIs
StatePublished - 2 Jan 2016

Keywords

  • higher rank numerical radius
  • higher rank numerical range
  • k-numerical radius
  • k-numerical range
  • numerical radius
  • numerical range

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