Interpolation classes and matrix monotone functions
Ameur, Yacin; Kaijser, Sten; Silvestrov, Sergei (2007). Interpolation classes and matrix monotone functions. Journal of Operator Theory, 57, (2), 409 - 427
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Published
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English
Authors:
Ameur, Yacin
;
Kaijser, Sten
;
Silvestrov, Sergei
Department:
Non-commutative Geometry-lup-obsolete
Mathematics (Faculty of Engineering)
Research Group:
Non-commutative Geometry-lup-obsolete
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.
Keywords:
interpolation function ;
matrix monotone function ;
Pick function
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