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\noindent\parbox{2.95cm}{\includegraphics*[keepaspectratio=true,scale=0.125]{AFA.jpg}}
\noindent\parbox{4.85in}{\hspace{0.1mm}\\[1.5cm]\noindent
\qquad Ann. Funct. Anal. 3 (2012), no. 1, 121--127\\
{\footnotesize \qquad \textsc{\textbf{$\mathscr{A}$}nnals of
\textbf{$\mathscr{F}$}unctional
\textbf{$\mathscr{A}$}nalysis}\\
\qquad ISSN: 2008-8752 (electronic)\\
\qquad URL:
\textcolor[rgb]{0.00,0.00,0.99}{www.emis.de/journals/AFA/}
}\\[.5in]}

\title[Compactness in complex interpolation]{On compactness in
complex interpolation}

\author[J. Voigt]{J\"urgen Voigt}

\address{Fachrichtung Mathematik, Technische Universit\"at Dresden,
01062 Dresden, Germany.}
\email{\textcolor[rgb]{0.00,0.00,0.84}{juergen.voigt@tu-dresden.de}}

\dedicatory{{\rm Communicated by D. Werner }}

\subjclass[2010]{Primary 46B70; Secondary 47B07.}

\keywords{Complex interpolation, compact operator function.}

\date{Received: 4 January 2012; Accepted: 7 February 2012.}

\begin{abstract}
We show that, in complex interpolation, an operator function that is compact
on one side of the interpolation scale will be compact for all proper
interpolating
spaces if the right hand side $(Y^0,Y^1)$ is reduced to a single space.
A corresponding result, in restricted generality, is shown if the left hand side
$(X^0,X^1)$ is reduced to a single space.
These results are derived from the fact that a holomorphic operator valued
function on an open subset of $\C$ which
takes values in the compact operators on part of the boundary is in fact compact
operator valued.
\end{abstract} \maketitle
\vspace{2in}
\end{document}

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