Abstract
This paper contains a collection of open problems related to composition operators and weighted composition operators acting on spaces of analytic functions, predominantly on the Hilbert Hardy space H2 over the open unit disc. Some are related to the invariant subspaces of composition operators, some to the spectra and numerical ranges of such operators, others are related to the connection of certain weighted composition on H2 and the unweighted composition operators on Hardy–Smirnov spaces, or the connection of composition operators with asymptotically Toeplitz operators. The problems raised are open to the knowledge of this author, and interesting, in his opinion.
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