Characterizations of L 1 -predual spaces by centerable subsets

Yanzheng Duan; Bor-Luh Lin

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 2, page 239-243
  • ISSN: 0010-2628

Abstract

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In this note, we prove that a real or complex Banach space X is an L 1 -predual space if and only if every four-point subset of X is centerable. The real case sharpens Rao’s result in [Chebyshev centers and centerable sets, Proc. Amer. Math. Soc. 130 (2002), no. 9, 2593–2598] and the complex case is closely related to the characterizations of L 1 -predual spaces by Lima [Complex Banach spaces whose duals are L 1 -spaces, Israel J. Math. 24 (1976), no. 1, 59–72].

How to cite

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Duan, Yanzheng, and Lin, Bor-Luh. "Characterizations of $L^1$-predual spaces by centerable subsets." Commentationes Mathematicae Universitatis Carolinae 48.2 (2007): 239-243. <http://eudml.org/doc/250226>.

@article{Duan2007,
abstract = {In this note, we prove that a real or complex Banach space $X$ is an $L^1$-predual space if and only if every four-point subset of $X$ is centerable. The real case sharpens Rao’s result in [Chebyshev centers and centerable sets, Proc. Amer. Math. Soc. 130 (2002), no. 9, 2593–2598] and the complex case is closely related to the characterizations of $L^1$-predual spaces by Lima [Complex Banach spaces whose duals are $L_1$-spaces, Israel J. Math. 24 (1976), no. 1, 59–72].},
author = {Duan, Yanzheng, Lin, Bor-Luh},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Chebyshev radius; centerable subsets and $L^1 $-predual spaces; Chebyshev radius},
language = {eng},
number = {2},
pages = {239-243},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Characterizations of $L^1$-predual spaces by centerable subsets},
url = {http://eudml.org/doc/250226},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Duan, Yanzheng
AU - Lin, Bor-Luh
TI - Characterizations of $L^1$-predual spaces by centerable subsets
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 2
SP - 239
EP - 243
AB - In this note, we prove that a real or complex Banach space $X$ is an $L^1$-predual space if and only if every four-point subset of $X$ is centerable. The real case sharpens Rao’s result in [Chebyshev centers and centerable sets, Proc. Amer. Math. Soc. 130 (2002), no. 9, 2593–2598] and the complex case is closely related to the characterizations of $L^1$-predual spaces by Lima [Complex Banach spaces whose duals are $L_1$-spaces, Israel J. Math. 24 (1976), no. 1, 59–72].
LA - eng
KW - Chebyshev radius; centerable subsets and $L^1 $-predual spaces; Chebyshev radius
UR - http://eudml.org/doc/250226
ER -

References

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  5. Hustad O., Intersection properties of balls in complex Banach spaces whose dual are L 1 -spaces, Acta Math. 132 (1974), 282-313. (1974) MR0388049
  6. Lacey H.E., The isometric theory of classical Banach spaces, Grundlehren Math. Wiss., Band 208, Springer, New York-Heidelberg, 1974. Zbl0285.46024MR0493279
  7. Lima A., Complex Banach spaces whose duals are L 1 -spaces, Israel J. Math. 24 (1976), 1 59-72. (1976) Zbl0334.46014MR0425584
  8. Lima A., Intersection properties of balls and subspaces in Banach spaces, Trans. Amer. Math. Soc. 227 (1977), 1-62. (1977) Zbl0347.46017MR0430747
  9. Lindenstrauss J., Extension of compact operators, Mem. Amer. Math. Soc., Vol. 48, Provindence, 1964. Zbl0141.12001MR0179580
  10. Rao T.S.S.R.K., Chebyshev centers and centerable sets, Proc. Amer. Math. Soc. 130 (2002), 9 2593-2598. (2002) MR1900866

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