# On Certain Higher Order Riccati-Type Operator Equations with Possibly Unbounded Operator Coefficients

### Tapas Mazumdar

Wright State University, Dayton, USA

## Abstract

Let $\mathcal H$ and $\mathcal V^1$ be complex Hilbert spaces, with $\mathcal V^1$ topologically included in $\mathcal H$, and $\mathcal V^2$ a complex pre-Hilbert space. There is considered the existence of a solution $X = X_Q \in \mathcal L (\mathcal V^2, \mathcal V^1)$ of the operator equation

in the space of (bounded or not) linear operators in $\mathcal H$ under the data $A_1, B_1 \in \mathcal L (\mathcal V^1, \mathcal H), D, E, F \in \mathcal L (\mathcal V^1, \mathcal V^2); A_2, B_2: \mathcal V^2 \to \mathcal V^2$ linear and $Q \in \mathcal L (\mathcal V^2, \mathcal H)$ one-dimensional. Under some hypotheses, an iterative analytic metiod to arrive at the existence of such a solution is given. Two examples are given.

## Cite this article

Tapas Mazumdar, On Certain Higher Order Riccati-Type Operator Equations with Possibly Unbounded Operator Coefficients. Z. Anal. Anwend. 6 (1987), no. 5, pp. 409–419

DOI 10.4171/ZAA/260