Extending positive definiteness
Functional Analysis
2009-07-01 v1
Abstract
The main result of the paper gives criteria for extendibility of sesquilinear form-valued mappings defined on symmetric subsets of *-semigroups to positive definite ones. By specifying this we obtain new solutions of: * the truncated complex moment problem, * the truncated multidimensional trigonometric moment problem, * the truncated two-sided complex moment problem, as well as characterizations of unbounded subnormality and criteria for the existence of unitary power dilation.
Cite
@article{arxiv.0906.5410,
title = {Extending positive definiteness},
author = {D. Cichoń and J. Stochel and F. H. Szafraniec},
journal= {arXiv preprint arXiv:0906.5410},
year = {2009}
}