Abstract
Let \(C_{\varphi }\) be the composition operator with monomial symbol \(\varphi (z)=z^m\), \(z\in \mathbb {D}\), for some positive integer m. In this article, we investigate the point spectrum, spectrum, and essential spectrum of the operators \(C_{\varphi }^*C_{\varphi }\), \(C_{\varphi }C_{\varphi }^*\), self-commutator \([C_{\varphi }^*,C_{\varphi }]\) and anti-self-commutator \(\{C_{\varphi }^*,C_{\varphi }\}\) on weighted Hardy spaces \(H^2(\beta )\) and recover known results for the classical Hardy, Bergman, and Dirichlet spaces.
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Heller, K.C., Pons, M.A. Composition Operators with Monomial Symbol Acting on Weighted Hardy Spaces. Mediterr. J. Math. 15, 2 (2018). https://doi.org/10.1007/s00009-017-1040-5
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DOI: https://doi.org/10.1007/s00009-017-1040-5