The Stieltjes moment problem in vector lattices

Kusraev A. G. , Malyugin S. A.
Владикавказский математический журнал. . Том 1. 1999 г.. Выпуск 1.

Аннотация:
In the present paper the Stieltjes moment problem in vector lattices is briefly outlined.First of all two examples justifying the statement of the moment problem in vector lattices are considered. The first example concerns a stochastic setting of the moment problem (the moment sequence depends on a measurable parameter) and the second one concerns the spectral resolution of a self-adjoint operator in a Hilbert space. Both examples are covered by the Freudenthal spectral theorem, which is one of the most powerful tools in the theory of vector lattices, and can be interpreted as one of the first solutions to the moment problem in vector lattices. In the last section two resulats concerning the general Stieltjes moment problem in vector lattices are formulated. The main difficulty is to find an appropriate measure extension in vector lattices.

Язык статьи: Английский Загрузить полный текст