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Interpolation classes and matrix monotone functions
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2007 (English)In: Journal of operator theory, ISSN 0379-4024, E-ISSN 1841-7744, Vol. 57, no 2, p. 409-427Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2007. Vol. 57, no 2, p. 409-427
Keywords [en]
interpolation function, matrix monotone function, Pick function
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-143633ISI: 000248611300010OAI: oai:DiVA.org:uu-143633DiVA, id: diva2:390813
Available from: 2011-01-24 Created: 2011-01-24 Last updated: 2017-12-11Bibliographically approved

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