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 Ba(T ) be the set of its analytic bounded point evaluations. J. B. Conway asked if the interior of B(T ) and Ba(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 (β), and we show that Ba(T )\Λ = int(B(T ))\Λ, with different subsets Λ in σ(T ).Mathematics Subject Classification. Primary 47B.

Let B(O 2 ) = {x ∈ O 2 , | x |< 1} be the bounded realization of the exceptional symmetric space F 4(−20) /Spin(9). For a nonzero real number λ, we give a necessary and a sufficient condition on eigenfunctions F of the Laplace-Beltrami operator on B(O 2 ) with eigenvalue −(λ 2 + ρ 2 ) to have an L p -Poisson integral representations on the boundary ∂B(O 2 ). Namely, F is the Poisson integral of an L p -function on the boundary if and only if it satisfies the following growth condition of Hardy-type:This extends previous results by the first author et al. for classical hyperbolic spaces.

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