# Lund University Publications

## LUND UNIVERSITY LIBRARIES

### Interpolation classes and matrix monotone functions

(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)
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.pdf
2016-04-01 17:05:30
date last changed
2020-01-12 20:02:33
@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},
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.pdf},
volume       = {57},
year         = {2007},
}