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Copies of $ l\sb \infty$ in $ L\sp p(\mu;X)$

Author: José Mendoza
Journal: Proc. Amer. Math. Soc. 109 (1990), 125-127
MSC: Primary 46E40; Secondary 46B20
MathSciNet review: 1012935
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Abstract: Let $ X$ be a Banach space and let $ (\Omega ,\sum ,\mu )$ be a measure space. For $ 1 \leq p < + \infty $ we denote by $ {L^p}(\mu ;X)$ the Banach space of all $ X$-valued Bochner $ p$-integrable functions on $ \Omega $. In this note we show that $ {L^p}(\mu ;X)$ contains an isomorphic copy of $ {l_\infty }$ if and only if $ X$ does.

References [Enhancements On Off] (What's this?)

  • [1] J. Diestel and J. J. Uhl Jr., Vector measures, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis; Mathematical Surveys, No. 15. MR 0453964
  • [2] L. Drewnowski, Copies of $ {l_\infty }$ in the operator space $ {K_w} * ({X^*},Y)$, (to appear).
  • [3] N. Dunford and J. T. Schwartz, Linear operators, vol. I. New York, Interscience, 1955.
  • [4] N. J. Kalton, Spaces of compact operators, Math. Ann. 208 (1974), 267–278. MR 0341154,
  • [5] S. Kwapien, Sur les espaces de Banach contenant $ {c_0}$, Studia Math. 52 (1974), 187-188.
  • [6] S. Lang, Analysis II, Addison-Wesley, Reading, MA, 1969.
  • [7] Gilles Pisier, Une propriété de stabilité de la classe des espaces ne contenant pas 𝑙¹, C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 17, A747–A749 (French, with English summary). MR 0511805
  • [8] Haskell P. Rosenthal, On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37 (1970), 13–36. MR 0270122,

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