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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, 59--67\\
$\frac{\rule{4.55in}{0.05in}}{{}}$\\
{\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[Operator-valued innner product]{Operator-valued inner product and operator inequalities}

\author[J.I. Fujii]{Jun Ichi Fujii$^1$}

\address{$^{1}$ Department of Arts and Sciences (Information Science), Osaka Kyoiku University, Asahigaoka,
Kashiwara, Osaka 582-8582, Japan.}

\email{\textcolor[rgb]{0.00,0.00,0.84}{fujii@cc.osaka-kyoiku.ac.jp}}


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

\subjclass[2000]{Primary 47A63; Secondary 47A75, 47A80.}

\keywords{Schwarz inequality, Jensen inequality, Operator
inequality.}

\date{Received: 29 March 2008; Accepted 13 May 2008}.

\begin{abstract}
The Schwarz inequality and Jensen's one are fundamental in  a
Hilbert space. Regarding a sesquilinear map $B(X,Y)=Y^*X$ as an
operator-valued inner product, we discuss operator versions for the
above inequalities and give simple conditions that the equalities
hold.
\end{abstract} \maketitle
\vspace{1.5in}
\end{document}

.
