The analytic Radon-Nikodým property in Lebesgue Bochner function spaces

Dowling, Patrick N.

doi:10.1090/S0002-9939-1987-0866440-5

The analytic Radon-Nikodým property in Lebesgue Bochner function spaces
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Proc. Amer. Math. Soc. 99 (1987), 119-122 Request permission

Abstract:

Let $X$ be a complex Banach space, $(\Omega ,\sum ,\mu )$ a finite measure space, and $1 \leq p < \infty$. Then ${L_p}(\mu ;X)$ has the analytic Radon-Nikodym property if and only if $X$ has it.

References

Volker Aurich, Bounded holomorphic embeddings of the unit disk into Banach spaces, Manuscripta Math. 45 (1983), no. 1, 61–67. MR 722922, DOI 10.1007/BF01168580
A. V. Bukhvalov and A. A. Danilevich, Boundary properties of analytic and harmonic functions with values in a Banach space, Mat. Zametki 31 (1982), no. 2, 203–214, 317 (Russian). MR 649004
J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964, DOI 10.1090/surv/015
Seán Dineen, Complex analysis in locally convex spaces, Notas de Matemática [Mathematical Notes], vol. 83, North-Holland Publishing Co., Amsterdam-New York, 1981. MR 640093
Patrick N. Dowling, Representable operators and the analytic Radon-Nikodým property in Banach spaces, Proc. Roy. Irish Acad. Sect. A 85 (1985), no. 2, 143–150. MR 845538
G. A. Edgar, Complex martingale convergence, Banach spaces (Columbia, Mo., 1984) Lecture Notes in Math., vol. 1166, Springer, Berlin, 1985, pp. 38–59. MR 827757, DOI 10.1007/BFb0074691

Analytic martingale convergence

Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR 0089373