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Spectral properties of certain operators on Hardy spaces of planar regions. (English) Zbl 0658.47028
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.
Reviewer: Yu.Latushkin

MSC:
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
47B38 Linear operators on function spaces (general)
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