The present lectures are based on a course deli vered by the authors at
the Uni versi ty of Bucharest, in the winter semester 1985-1986. Without
aiming at completeness, the topics selected cover all the major
questions concerning hyponormal operators. Our main purpose is to
provide the reader with a straightforward access to an active field of
research which is strongly related to the spectral and perturbation
theories of Hilbert space operators, singular integral equations and
scattering theory. We have in view an audience composed especially of
experts in operator theory or integral equations, mathematical
physicists and graduate students. The book is intended as a reference
for the basic results on hyponormal operators, but has the structure of
a textbook. Parts of it can also be used as a second year graduate
course. As prerequisites the reader is supposed to be acquainted with
the basic principles of functional analysis and operator theory as
covered for instance by Reed and Simon [1]. A t several stages of
preparation of the manuscript we were pleased to benefit from proper
comments made by our cOlleagues: Grigore Arsene, Tiberiu Constantinescu,
Raul Curto, Jan Janas, Bebe Prunaru, Florin Radulescu, Khrysztof Rudol,
Konrad Schmudgen, Florian-Horia Vasilescu. We warmly thank them all. We
are indebted to Professor Israel Gohberg, the editor of this series, for
his constant encouragement and his valuable mathematical advice. We wish
to thank Mr. Benno Zimmermann, the Mathematics Editor at Birkhauser
Verlag, for cooperation and assistance during the preparation of the
manuscript.