Spectral properties of certain operators on Hardy spaces of planar regions (Q1111148)

The essential spectrum of the multiplication operator \(M_{\phi}f=\phi f\) on Hardy space \(H^ p(G)\), \(1\leq p\leq \infty\) is calculated. Here \(\phi\) is any bounded analytic function on any region G in the complex plane. The special case in which G is bounded and \(\phi (z)=z\) is studied in detail.