Interpolation classes and matrix monotone functions
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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 Cn of interpolation functions of order n coincides with the class of functions /+ such that for each nsubset 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 Cn and their relations to matrix monotone functions of finite order. We also consider interpolation functions on general unital C*algebras.
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Research areas and keywords  Subject classification (UKÄ) – MANDATORY
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Original language  English 

Pages (fromto)  409427 
Journal  Journal of Operator Theory 
Volume  57 
Issue number  2 
Publication status  Published  2007 
Publication category  Research 
Peerreviewed  Yes 