Interpolation classes and matrix monotone functions
(2007) In Journal of Operator Theory 57(2). p.409427 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... (More)
 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/657142
 author
 Ameur, Yacin ; Kaijser, Sten and Silvestrov, Sergei ^{LU}
 organization
 publishing date
 2007
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 interpolation function, matrix monotone function, Pick function
 in
 Journal of Operator Theory
 volume
 57
 issue
 2
 pages
 409  427
 publisher
 Theta Foundation
 external identifiers

 wos:000248611300010
 scopus:34548844182
 ISSN
 03794024
 language
 English
 LU publication?
 yes
 id
 593e7b237ca84c9cb83f161938cb0390 (old id 657142)
 alternative location
 http://www.mathjournals.org/jot/2007057002/2007057002010.pdf
 date added to LUP
 20160401 17:05:30
 date last changed
 20200112 20:02:33
@article{593e7b237ca84c9cb83f161938cb0390, 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.}, author = {Ameur, Yacin and Kaijser, Sten and Silvestrov, Sergei}, issn = {03794024}, language = {eng}, number = {2}, pages = {409427}, publisher = {Theta Foundation}, series = {Journal of Operator Theory}, title = {Interpolation classes and matrix monotone functions}, url = {http://www.mathjournals.org/jot/2007057002/2007057002010.pdf}, volume = {57}, year = {2007}, }