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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Orlicz-Pettis theorem fails for Lumer's Hardy spaces $ (LH)\sp p(B)$


Author: M. Nawrocki
Journal: Proc. Amer. Math. Soc. 109 (1990), 957-963
MSC: Primary 46E15
MathSciNet review: 1007507
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Abstract: In this paper we prove that if $ n > 1$ and $ 0 < p < 1$ then the Lumer's Hardy space $ {(LH)^p}({{\mathbf{B}}_n})$ of the unit ball $ {{\mathbf{B}}_n}$ in $ {{\mathbf{C}}^n}$ does not have the Orlicz-Pettis property.


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  • [1] L. Drewnowski, Un thèorème sur les opèrateurs de $ {l_\infty }(\Gamma )$, C. R. Acad. Sci. Paris A 281 (1985), 967-969. MR 0385626 (52:6486)
  • [2] P. L. Duren, B. W. Romberg, and A. L. Shields, Linear functionals of $ {H^p}$ with $ 0 < p < 1$, J. Reine Angew. Math. 238 (1969), 32-60. MR 0259579 (41:4217)
  • [3] N. J. Kalton, Subseries convergence in topological groups and vector measures, Israel J. Math. 10 (1971), 402-412. MR 0294558 (45:3628)
  • [4] -, The Orlicz-Pettis theorem, Amer. Math. Soc., Contemp Math. 2 (1980), 91-100. MR 621853 (82g:46027)
  • [5] N. J. Kalton, N. T. Peck, and J. W. Roberts, An $ F$-spaces sampler, London Math. Soc. Lecture Notes 89 (1984). MR 808777 (87c:46002)
  • [6] G. Lumer, Espaces de Hardy en plusieurs variables complexes, C. R. Acad Sci. Paris 273 (1971), 151-154. MR 0282208 (43:7921)
  • [7] M. Nawrocki, On the Orlicz-Pettis property in nonlocally convex $ F$-spaces, Proc. Amer. Math. Soc. 101 (1987), 492-496. MR 908655 (88k:46002)
  • [8] W. Rudin, Lumer's Hardy spaces, Michigan Math. J. 24 (1977), 1-5. MR 0444993 (56:3338)
  • [9] -, Grundlehren der matematischen Wissenschaften 241, Springer-Verlag, Berlin, 1980.
  • [10] J. H. Shapiro, Some $ F$-spaces of harmonic functions for which the Orlicz-Pettis theorem fails, Proc. London Math. Soc. 50 (1985), 299-313. MR 772715 (86i:46023)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1007507-0
PII: S 0002-9939(1990)1007507-0
Keywords: Oricz-Pettis theorem, Lumer's Hardy spaces
Article copyright: © Copyright 1990 American Mathematical Society