Norms of Moore-Penrose Inverses of Fredholm Toeplitz Operators

Abstract.

In this paper we estimate the norm of the Moore-Penrose inverse T(a)⁺ of a Fredholm Toeplitz operator T(a) with a matrix-valued symbol a∈L ^∞_{N ×  N} defined on the complex unit circle. In particular, we show that in the ”generic case” the strict inequality ||T(a)⁺|| > ||a⁻¹||_∞ holds. Moreover, we discuss the asymptotic behavior of ||T(t^ra)⁺|| for $r\, \in \,\user2{\mathbb{Z}}$. The results are illustrated by numerical experiments.