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We describe the geometrical structure on a complex quasi-Banach space that is necessay and sufficient for the existence of boundary limits for bounded, -valued analytic functions on the open unit disc of the complex plane. It is shown that in such spaces, closed bounded subsets have many and that bounded upper semi-continuous functions on these sets have arbitrarily small plurisubharmonic perturbations that attain their maximum. This yields a certain representation of the unit ball of in a...
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