Dowling, P. N.; Edgar, G. A. Some characterizations of the analytic Radon-Nikodým property in Banach spaces. (English) Zbl 0664.46016 J. Funct. Anal. 80, No. 2, 349-357 (1988). A Banach space X for which every bounded X-valued analytic function on the open unit disk has radial limits almost everywhere is said to have the analytic Radon-Nikodym property (aRNP). It is shown that X has aRNP if every operator from \(L^ 1\) to X which factors through \(L^ 1/H^ 1_ 0\) is representable, a characterization which is similar to that of RNP. Some immediate applications to properties of subspaces of \(L^ 1/H^ 1_ 0\) are indicated. The characterization also gives rise to a reasonable definition of aRNP for real spaces. Reviewer: E.Behrends Cited in 3 Documents MSC: 46B22 Radon-Nikodým, Kreĭn-Milman and related properties Keywords:analytic Radon-Nikodym property PDFBibTeX XMLCite \textit{P. N. Dowling} and \textit{G. A. Edgar}, J. Funct. Anal. 80, No. 2, 349--357 (1988; Zbl 0664.46016) Full Text: DOI References: [1] Bourgain, J., Dunford-Pettis operators on \(L_1\) and the Radon-Nikodým property, Israel J. Math., 37, 34-47 (1980) · Zbl 0457.46017 [2] Bourgin, R. D., Geometric Aspects of Convex Sets with the Radon-Nikodým Property, (Lecture Notes in Mathematics, Vol. 993 (1983), Springer-Verlag: Springer-Verlag New York/Berlin) · Zbl 0512.46017 [3] Bukhvalov, A. V.; Danilevich, A. A., Math. Notes, 31, 104-110 (1982), English translation · Zbl 0496.30029 [4] Diestel, J.; Uhl, J. J., Vector Measures, (Mathematical Surveys, Vol. 15 (1977), Amer. Math. Soc: Amer. Math. Soc Providence, RI) · Zbl 0369.46039 [5] Dowling, P. N., Representable operators and the analytic Radon-Nikodým property in Banach spaces, (Proc. Roy. Irish Acad. Sect. A, 85 (1985)), 143-150 · Zbl 0607.46016 [6] Dowling, P. N., The Analytic Radon-Nikodým Property in Banach Spaces, (Thesis (1986), Kent State University) · Zbl 0664.46016 [7] Edgar, G. A., Analytic martingale convergence, J. Funct. Anal., 69, 268-280 (1986) · Zbl 0605.60050 [8] Ghoussoub, N.; Rosenthal, H. P., Martingales, \(G_δ\)-embeddings and quotients of \(L^1\), Math. Ann., 264, 321-332 (1983) · Zbl 0511.46017 [9] Hensgen, W., Hardy-Räume vektorwertiger Funktionen, Thesis (1986), Munich · Zbl 0594.46028 [10] Linde, W., An operator ideal in connection with the Radon-Nikodým property of Banach spaces, Math. Nachr., 71, 65-73 (1976) · Zbl 0328.47011 [11] Pelczynski, A., Banach spaces of analytic functions and absolutely summing operators, (CBMS Regional Conf. Ser. in Math., 30 (1977)) · Zbl 0475.46022 [12] Pietsch, A., Operator Ideals (1980), North-Holland: North-Holland Amsterdam · Zbl 0399.47039 [13] Reinov, O. J., Soviet Math. Dokl., 16, 119-123 (1975), English translation · Zbl 0317.47022 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.