Interpolation classes and matrix monotone functions

Yacin Ameur, Sten Kaijser, Sergei Silvestrov

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7 Citations (SciVal)

Abstract

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.
Original languageEnglish
Pages (from-to)409-427
JournalJournal of Operator Theory
Volume57
Issue number2
Publication statusPublished - 2007

Subject classification (UKÄ)

  • Mathematics

Keywords

  • interpolation function
  • matrix monotone function
  • Pick function

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