JournalsrmiVol. 38, No. 3pp. 731–759

Noncommutative partially convex rational functions

  • Michael Jury

    University of Florida, Gainesville, USA
  • Igor Klep

    University of Ljubljana, Slovenia
  • Mark E. Mancuso

    Lafayette College, Easton, USA
  • Scott McCullough

    University of Florida, Gainesville, USA
  • James Eldred Pascoe

    University of Florida, Gainesville, USA
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Abstract

Motivated by classical notions of bilinear matrix inequalities (BMIs) and partial convexity, this article investigates partial convexity for noncommutative functions. It is shown that noncommutative rational functions that are partially convex admit novel butterfly-type realizations that necessitate square roots. A strengthening of partial convexity arising in connection with BMIs – xyxy-convexity – is also considered. A characterization of xyxy-convex polynomials is given.

Cite this article

Michael Jury, Igor Klep, Mark E. Mancuso, Scott McCullough, James Eldred Pascoe, Noncommutative partially convex rational functions. Rev. Mat. Iberoam. 38 (2022), no. 3, pp. 731–759

DOI 10.4171/RMI/1304