Abstract
Let T be a bounded rationally multicyclic operator on some separable Banach space X, B(T) be the set of its bounded point evaluations and B a (T) be the set of its analytic bounded point evaluations. J. B. Conway asked if the interior of B(T) and B a (T) coincide for arbitrary subnormal operators on Hilbert spaces. Here, we are interested in Conway’s problem. We provide an example that answers negatively Conway’s question in the more general setting of operators satisfying Bishop’s property \({(\beta)}\), and we show that \({B_a(T) {\setminus} \Lambda = {\rm int}(B(T)){\setminus} \Lambda }\), with different subsets Λ in \({\sigma}\)(T).
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The first author was partially supported by the I+D MEC project MTM 2010-17687 and the third author was supported by the project URAC 03 and the project of Hassan II Academy of Sciences And Technology. The authors are thankful to the anonymous referee for his careful reading and valuable suggestions and remarks that improved this paper.
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Mbekhta, M., Ourchane, N. & Zerouali, E.H. The Interior of Bounded Point Evaluations for Rationally Cyclic Operators. Mediterr. J. Math. 13, 1981–1996 (2016). https://doi.org/10.1007/s00009-015-0585-4
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DOI: https://doi.org/10.1007/s00009-015-0585-4