Orthogonally additive and orthogonally multiplicative holomorphic functions of matrices

Qingying Bu, C J LIAO, Ngai Ching Wong*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

4 Citations (Scopus)

Abstract

Let H : Mm → Mm be a holomorphic function of the algebra Mm of complex m×m matrices. Suppose that H is orthogonally additive and orthogonally multiplicative on self-adjoint elements. We show that either the range of H consists of zero trace elements, or there is a scalar sequence {λn} and an invertible S in Mm such that. Here, xt is the transpose of the matrix x. In the latter case, we always have the first representation form when H also preserves zero products. We also discuss the cases where the domain and the range carry different dimensions.

Original languageEnglish
Pages (from-to)80-89
Number of pages10
JournalAnnals of Functional Analysis
Volume5
Issue number2
DOIs
Publication statusPublished - 2014

Scopus Subject Areas

  • Analysis
  • Anatomy
  • Algebra and Number Theory

User-Defined Keywords

  • Holomorphic functions
  • Homogeneous polynomials
  • Matrix algebras
  • Orthogonally additive and multiplicative
  • Zero product preserving

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