Corrections to the paper ``Roots of scalar operator-valued analytic functions and their functional calculus''

Abstract

Let X be a Banach space, T a linear bounded operator acting in X and / an analytic complex function defined in a neighborhood of σ(Γ). Let us suppose also that / is non-constant in each connected component of its domain of definition which intersects ύ{T). In this paper we study the spectral properties of T if f(T) is a spectral operator of scalar type. The example of Stampfli (see [18]) shows that in general T is not a scalar operator. We shall prove that T is a 0-scalar operator in the sense of [15], where Φ is a suitable basic algebra.