Fritzsche, Bernd; Kirstein, Bernd; Klotz, Lutz Completion of non-negative block operators in Banach spaces. (English) Zbl 0939.47002 Positivity 3, No. 4, 389-397 (1999). Let \({\mathcal B}\) be the direct sum of Banach spaces \({\mathcal B}_i\) \((i= 1,2,3)\), which is also a Banach space. A bounded linear operator \(A:{\mathcal B}\to{\mathcal B}^*\), where \({\mathcal B}^*\) is the Banach space of bounded antilinear functionals on \({\mathcal B}\), has a block representation \(A= (A_{jk})^3_{j,k}\), where \(A_{jk}:{\mathcal B}_k\to{\mathcal B}^*_j\) \((j,k= 1,2,3)\).The completion problem solved by the authors is: for given \(A_{j,k}\) \((j,k= 1,2)\) and \(A_{lm}\) \((l,m= 2,3)\) determine the set of all operators \(A_{13}\) and \(A_{31}\) such that \(A\) is a nonnegative operator (i.e. the functional \(Ax\geq 0\) for all \(x\in{\mathcal B}\)).This is a generalization of a finite-dimensional problem. A particular truncated trigonometric moment problem is also solved by means of the above result. Reviewer: D.Przeworska-Rolewicz (Warszawa) Cited in 1 Document MSC: 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A57 Linear operator methods in interpolation, moment and extension problems Keywords:block representation; completion problem; truncated trigonometric moment problem PDFBibTeX XMLCite \textit{B. Fritzsche} et al., Positivity 3, No. 4, 389--397 (1999; Zbl 0939.47002) Full Text: DOI