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Interpolation classes and matrix monotone functions

Ameur, Yacin; Kaijser, Sten and Silvestrov, Sergei LU (2007) In Journal of Operator Theory 57(2). p.409-427
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... (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 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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
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
0379-4024
language
English
LU publication?
yes
id
593e7b23-7ca8-4c9c-b83f-161938cb0390 (old id 657142)
alternative location
http://www.mathjournals.org/jot/2007-057-002/2007-057-002-010.pdf
date added to LUP
2007-12-05 09:35:03
date last changed
2017-01-01 07:23:58
@article{593e7b23-7ca8-4c9c-b83f-161938cb0390,
  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 &lt;= 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.},
  author       = {Ameur, Yacin and Kaijser, Sten and Silvestrov, Sergei},
  issn         = {0379-4024},
  keyword      = {interpolation function,matrix monotone function,Pick function},
  language     = {eng},
  number       = {2},
  pages        = {409--427},
  publisher    = {Theta Foundation},
  series       = {Journal of Operator Theory},
  title        = {Interpolation classes and matrix monotone functions},
  volume       = {57},
  year         = {2007},
}