Oka-analyticity of the essential spectrum (Q1113434)

Let X be a complex Banach space, C(X) the collection of all closed linear operators in X, and G an open set in \({\mathbb{C}}\). The author proves that: If \(z\in G\to T_ z\in C(X)\) is a holomorphic family, then \(z\in G\to \sigma (T_ z)\) is an analytic multifunction; where \(\sigma (T_ z)\) denotes the Wolf spectrum, Weyl spectrum or the Browder spectrum of \(T_ z\); which generalizes some results of Slodkowski.