Moment problems for commuting pairs of contractions
by
Doru Paunescu
Polytechnical Institute, Timisoara
Coauthors: Pasc Gavruta

Let H be a complex Hilbert space and L( H) the C ^* -algebra of all bounded linear operators on H; an element of ( L( H) ) ₁^- , the (closed) unit ball of L( H) , will be called contraction on H.

In 1982 Zoltán Sebestyén (see [2]) solved the following moment problem:

Given a sequence { h_n} _{n in N} of elements of the Hilbert space H under what condition does there exist a contraction T on H  such that

hn=Tnh0      \textholds for  n=1, 2, ...     ? \tag\QTRit1

(\theequation)

The key to the solutions is the theory of unitary dilations. His answer is the following:

Theorem. Let { h_m} _{m in N} be a sequence of elements of the Hilbert space H. There exists a contraction satisfying ( 1) if and only if

Date received: June 5, 2000