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\noindent\parbox{2.85cm}{\includegraphics*[keepaspectratio=true,scale=1.75]{BJMA.jpg}}
\noindent\parbox{4.85in}{\hspace{0.1mm}\\[1.5cm]\noindent
Banach J. Math. Anal. 2 (2008), no. 2, 1--8\\
$\frac{\rule{4.55in}{0.05in}}{{}}$\\
{\footnotesize
\textcolor[rgb]{0.65,0.00,0.95}{\textsc{\textbf{\large{B}}anach
\textbf{\large{J}}ournal of \textbf{\large{M}}athematical
\textbf{\large{A}}nalysis}}\\
ISSN: 1735-8787 (electronic)\\
\textcolor[rgb]{0.00,0.00,0.84}{\textbf{http://www.math-analysis.org }}\\
$\frac{{}}{\rule{4.55in}{0.05in}}$}\\[.5in]}

\title{Positivity of operator-matrices of Hua-type}

\author[T. Ando]{Tsuyoshi Ando}

\address{Shiroishi-ku, Hongo-dori 9, Minami 4-10-805, Sapporo 003-0024, Japan.}

\email{\textcolor[rgb]{0.00,0.00,0.84}{ando@es.hokudai.ac.jp}}

\dedicatory{This paper is dedicated to Professor Josip E. Pe\v{c}ari\'{c}\\
\vspace{.5cm} {\rm Submitted by F. Kittaneh}}

\subjclass[2000]{Primary 47B63; Secondary 47B15, 15A45.}

\keywords{Positivity, Strict contraction, Operator-matrix, Hua theorem.}

\date{Received: 1 March 2008; Accepted 25 March 2008.}

\begin{abstract}
Let $A_j\,\,(j = 1, 2,\ldots , n)$ be strict contractions on a Hilbert space.
We study an $n \times n$ operator-matrix:
\[\textbf{H}_n(A_1,A_2,\ldots ,A_n) = [(I - A^*_j A_i)^{-1}]^n_{i,j=1}.\]
For the case $n = 2$, Hua [Inequalities involving determinants, Acta Math. Sinica, 5 (1955), 463--470 (in Chinese)] proved positivity, i.e., positive semi-definiteness of $\textbf{H}_2(A_1,A_2)$. This is, however, not always true for $n = 3$. First we generalize a known condition which guarantees positivity of $\textbf{H}_n$. Our main result is that positivity of $\textbf{H}_n$ is preserved under the operator M\"obius map of the open unit
disc $\mathcal D$ of strict contractions.
\end{abstract} \maketitle

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