Communications of the
Korean Mathematical Society CKMS

In this paper, we show that if ${\mathcal A}$ is a differential subalgebra of Banach algebras ${\mathcal B}(\ell^r)$, $1\le r\le \infty$, then solutions of the infinite dimensional linear system associated with a matrix in ${\mathcal A}$ have its $p$-exponential stability being equivalent to each other for different $1\le p\le \infty$.

Keywords: infinite matrix, differential subalgebra, Lyapunov equation, linear system, exponential stability

MSC numbers: 34M10, 34D20, 46A45