| Title | Interpolation classes and matrix monotone functions |
| Authors | Yacin Ameur, Sten Kaijser, Sergei Silvestrov |
| Alternative Location | http://www.mathjournals.org... |
| Publication | Journal of Operator Theory |
| Year | 2007 |
| Volume | 57 |
| Issue | 2 |
| Pages | 409 - 427 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Theta Foundation |
| Abstract English | An interpolation function of order n is a positive function -/+ on (0, infinity) such that vertical bar vertical bar -/+ (A)(1/2) T -/+ (A)-(1/2) vertical bar vertical bar <= max(vertical bar vertical bar T vertical bar vertical bar, vertical bar A(1/2)TA(-1/2) vertical bar vertical bar) for all n x ii matrices T and A such that A is positive definite. By a theorem of Donoghue, the class C-n of interpolation functions of order n coincides with the class of functions -/+ such that for each n-subset S = {lambda i}(n)(i=1)of (0,infinity) there exists a positive Pick function h on (0, co) interpolating -/+ at S. This note comprises a study of the classes C-n and their relations to matrix monotone functions of finite order. We also consider interpolation functions on general unital C*-algebras. |
| Keywords | interpolation function, matrix monotone function, Pick function, |
| ISBN/ISSN/Other | ISSN: 0379-4024 |
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