Abstract
There is a countable cancellative commutative *-semigroup S withzero (in fact, a *-subsemigroup of G × N0 for some abelian group G carrying the inverse involution) such that the answer to the question “if f is a function on S , with values in Md(C) (the square matrices of order d) and such that $\sum^{n}_{j,k=1} \lbrak f(s^*_k s_j)\xi_j, \xi_k \rbrak \ge 0$ for all n in N, s1, . . . , sn in S , and $\xi_1$, . . . , $\xi_n$ in Cd, does it follow that $f(s) = \int_{S^*}\sigma (s) d\mu(\sigma) (s \memb S)$ for some measure $\mu$ (with values in Md(C)+ , the positive semidenite matrices) on the space S of hermitian multiplicative functions on S?” is “yes” if d = 1 but “no” if d = 2 (hence also for d > 2).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bisgaard, T. On the Relation between the Scalar Moment Problem and the Matrix Moment Problem on *-Semigroups. Semigroup Forum 68, 25–46 (2004). https://doi.org/10.1007/s00233-002-0003-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00233-002-0003-7