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Interpolation classes and matrix monotone functions

Ameur, Yacin LU ; 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
; and
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.html
http://www.mathjournals.org/jot/2007-057-002/2007-057-002-010.pdf
date added to LUP
2016-04-01 17:05:30
date last changed
2022-01-29 00:17:36
@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}},
  keywords     = {{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}},
  url          = {{http://www.mathjournals.org/jot/2007-057-002/2007-057-002-010.html}},
  volume       = {{57}},
  year         = {{2007}},
}