When are positive *-linear matrix maps also completely positive?
- Date: Wednesday 9 February 2022, 16:30 – 17:30
- Location: Online event
- Type: Analysis, Seminars, Pure Mathematics
- Cost: Free
Professor Sanne ter Horst (North-West University) will present his research in Analysis.
"There are many more positive maps than completely positive maps," see , there are also various applications in which positive linear matrix maps happen to be completely positive. One such instance is Nevanlinna-Pick interpolation, where a necessary and sufficient solution criteria can be phrased as a positivity condition (Lyapunov or Stein order, see ) while the more common Pick matrix criteria stems from complete positivity (via Choi's theorem). In this talk we analyze *-linear matrix maps (linear maps that preserve adjoints) via what we call Hill representations (after , see also ) and determine various classes of *-linear matrix maps under which positivity and complete positivity coincide . It is based on work with my PhD student Alma van der Merwe.
 R.D. Hill, Linear transformations which preserve hermitian matrices, Linear Algebra Appl. 6 (1973), 257--262.
 S. ter Horst and A. van der Merwe, A Hill-Pick matrix criteria for the Lyapunov order, submitted.
 S. ter Horst and A. van der Merwe, Hill representations for *-linear matrix maps, Indag. Math. (N.S.), to appear.
 S. ter Horst and A. van der Merwe, Linear matrix maps for which positivity and complete positivity coincide, Linear Algebra Appl. 628 (2021), 140--181.
 I. Klep, S. McCullough, K. Sivic, A. Zalar, There are many more positive maps than completely positive maps, Int. Math. Res. Not. 11 (2019) 3313--3375.
The talks are held using Zoom. Anyone interested in attending (outside the School of Mathematics) should email Ben Sharp at firstname.lastname@example.org to request zoom coordinates.