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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
DOI: https://doi.org/10.1090/S0002-9939-1990-1007507-0
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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DOI: https://doi.org/10.1090/S0002-9939-1990-1007507-0
Keywords: Oricz-Pettis theorem, Lumer's Hardy spaces
Article copyright: © Copyright 1990 American Mathematical Society