IJPAM: Volume 53, No. 1 (2009)

DIFFERENTIAL SYSTEMS ON SPACES OF
BOUNDED LINEAR OPERATORS

Fernanda Botelho$^1$, Annita Davis$^2$
$^{1,2}$Department of Mathematical Sciences
The University of Memphis
373, Dunn Hall, 3721, Norriswood St.,
Memphis, TN 38152-3240, USA
$^1$email: [email protected]
$^2$email: [email protected]


Abstract.We study systems of differential equations in $\mathcal{B}(\mathcal{H})$, the Banach space of bounded linear operators on a separable complex Hilbert space $ \mathcal{H} $, equipped with the standard operator norm. The systems considered in this paper are infinite dimensional generalizations of mathematical models of learning. We use the polar decomposition of operators to find an explicit form for solutions. We also discuss the usual questions of existence and uniqueness of solutions, as well as their stability behavior.

Received: April 13, 2009

AMS Subject Classification: 34G20, 47J25

Key Words and Phrases: nonlinear systems, bounded operators, complex Hilbert spaces, polar decomposition of operators

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 1