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Denting points in tensor products of Banach spaces


Author: Dirk Werner
Journal: Proc. Amer. Math. Soc. 101 (1987), 122-126
MSC: Primary 46B20; Secondary 46M05
DOI: https://doi.org/10.1090/S0002-9939-1987-0897081-1
MathSciNet review: 897081
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Abstract | References | Similar Articles | Additional Information

Abstract: Let dent $ A$ denote the set of denting points of a subset $ A$ of some Banach space. We prove

$\displaystyle {\text{dent cl co(}}K \otimes L) = {\text{dent }}K \otimes {\text{dent }}L$

for closed, bounded, absolutely convex subsets $ K$ and $ L$ of Banach spaces $ X$ and $ Y$. Here the closure refers to the completion of $ X \otimes Y$ w.r.t. some reasonable crossnorm.

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

  • [1] J. Bourgain and G. Pisier, A construction of $ {\mathcal{L}_\infty }$-spaces and related Banach spaces, Bol. Soc. Brasil. Mat. 14 (1983), 109-123. MR 756904 (86b:46021)
  • [2] R. D. Bourgin, Geometric aspects of convex sets with the Radon-Nikodým property, Lecture Notes in Math., Vol. 993, Springer-Verlag, Berlin and New York, 1983. MR 704815 (85d:46023)
  • [3] J. Diestel and J. J. Uhl, Vector measures, Math. Surveys, no. 15, Amer. Math. Soc., Providence, R.I., 1977. MR 0453964 (56:12216)
  • [4] M. Feder and P. Saphar, Spaces of compact operators and their dual spaces, Israel J. Math. 21 (1975), 28-49. MR 0377591 (51:13762)
  • [5] G. Godefroy, Nicely smooth Banach spaces, Longhorn Notes, The University of Texas at Austin Functional Analysis Seminar, 1984-1985, pp. 117-124. MR 832255
  • [6] G. Godefroy and P. Saphar, Duality in spaces of operators and smooth norms on Banach spaces (to appear). MR 955384 (89j:47026)
  • [7] S. Heinrich, Strongly exposed and conical points in a projective tensor product, Teor. Funksiĭ Funktsional. Anal. i Prilozhen. 22 (1975), 146-154. (Russian)
  • [8] W. M. Ruess and C. P. Stegall, Weak*-denting points in duals of operator spaces, Banach Spaces, Proc. Missouri Conf. Columbia 1984, Lecture Notes in Math., Vol. 1166, Springer-Verlag, Berlin and New York, 1986, pp. 158-168. MR 827769 (87k:47096)
  • [9] D. Werner and W. Werner, On the $ M$-structure of the operator space $ L\left( {CK} \right)$, Preprint.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0897081-1
Keywords: Denting point, tensor product
Article copyright: © Copyright 1987 American Mathematical Society

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