Operator moment problems in unbounded sets

The truncated complex $K$-moment problem

“…Concrete conditions (in terms of the β i ) for the existence of such a flat extension are given in [Fi1]. In [CuFi1] we proved that β (2n) has a representing measure supported in [a, b] if and only if there is an r-atomic representing measure supported in [a, b], and that this occurs if and only if H (n) ≥ 0 admits a flat extension for which bH (n) ≥ H x (n) ≥ aH (n); Theorem 5.5 thus refines this result in the case when r ≤ n. [PuVa2], [Rez], [StSz1], [StSz2], [Va1], [Va2]). For instance, a rather concrete Riesz-type condition is obtained in [PuVa1], when K is a compact semi-algebraic set.…”

Quantized moment problem

“…Recall that the operator moment problem [4] is to finding a positive operator-valued measure which express an integral representation for the given unital linear mapping from the algebra of all complex-valued polynomials in several real variables into the space of all sesquilinear forms on a pre-Hilbert space. Involving the fractional space technique [1,5,6], the operator moment problem has been solved in [1].…”

On Subnormality and Formal Subnormality for Tuples of Unbounded Operators

“…In general this property is false, even for two single operators : There exist commuting subnormal operators such that the bi-operator is not jointly subnormal (for more details see [12]). In a preceding work, (see [5], Theoreme 1.2 and Corollary 1.4) we have given characterizations of subnormal multi-operators (for similar results see [23] Theorem 3.4). We recall the statement of Theorem 1.2 from [5], for the convenience of the reader.…”

“…Some theoretical characterizations concerning the existence of a (jointly) normal extension for some tuples of unbounded operators have been given recently in [23], [24] and [5]. In the present paper, we introduce a notion of formally normal 268 Demanze IEOT multi-operator, and give a characterization of multi-operators having extensions of this kind.…”