Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Christian Wyss
Bergische Universität Wuppertal
Bounded solutions of operator Riccati equations
We consider Riccati equations of the form
A ∗ X + XA − XQ1X + Q2 = 0
for linear operators on a Hilbert space, where Q1 and Q2 are selfadjoint and nonnegative. Riccati equations
of this type are of interest e.g. in systems theory; in particular their bounded nonnegative solutions X.
However, in the general case there will also be unbounded solutions. We will study different methods to
characterise the boundedness of a solution X. Among the tools that we use are invariant subspaces of
the block operator matrix
Riesz bases, and indefinite inner products.
T =
�
A −Q1
−Q2 −A∗ �
,
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