Ando, Tsuyoshi Positivity of operator-matrices of Hua-type. (English) Zbl 1155.47019 Banach J. Math. Anal. 2, No. 2, 1-8 (2008). Given \(A_1,\dots,A_n\in B(H)\) strict contractions (i.e., \(\| A_i\| <1\)), the author considers the operator matrix \[ H_n(A_1,\dots,A_n)=[(I-A_j^*A_i)^{-1}]_{i,j=1}^n. \] L.K.Hua proved in [Acta Math.Sin.5, 463–470 (1955; Zbl 0066.26601)] that \(H_2(A_1,A_2)\) is positive-semidefinite. The author proved in [Linear Multilinear Algebra 8, 347–352 (1980; Zbl 0438.15019)] that the same is not necessarily true for \(H_3(A_1,A_2,A_3)\). In the paper under review, he shows a condition that guarantees positivity of \(H_n\), and he shows that positivity of \(H_n\) is preserved under the Möbius map (depending on the choice of a strict contraction \(B\)) \[ \Theta_B(Z)=(I-BB^*)^{-1/2}(B-Z)(I-B^*Z)(I-B^*B)^{1/2}. \] Reviewer: Martín Argerami (Regina) Cited in 8 Documents MSC: 47A63 Linear operator inequalities 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.) 15A45 Miscellaneous inequalities involving matrices Keywords:positivity; strict contraction; operator-matrix; Hua theorem Citations:Zbl 0066.26601; Zbl 0438.15019 PDFBibTeX XMLCite \textit{T. Ando}, Banach J. Math. Anal. 2, No. 2, 1--8 (2008; Zbl 1155.47019) Full Text: DOI EuDML EMIS