Abstract
In this chapter we collect a number of general concepts and simple facts on moment problems on commutative ∗-semigroups that will be used throughout the text, often without mention. Section 2.1 is about positive functionals on ∗-algebras and positive semidefinite functions on ∗-semigroups. In Sect. 2.2 we specialize to commutative ∗-algebras and ∗-semigroups and introduce moment functionals, moment functions, K-determinate moment functions, and generalized Hankel matrices. Some standard examples of commutative ∗-semigroups are given in Sect. 2.3.
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