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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/657142
- author
- Ameur, Yacin LU ; 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
- 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 <= 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}}, }