The reciprocal Dunford–Pettis property of order p in projective tensor products

Ioana Ghenciu

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 3, page 351-360
  • ISSN: 0010-2628

Abstract

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We investigate whether the projective tensor product of two Banach spaces X and Y has the reciprocal Dunford–Pettis property of order p , 1 p < , when X and Y have the respective property.

How to cite

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Ghenciu, Ioana. "The reciprocal Dunford–Pettis property of order $p$ in projective tensor products." Commentationes Mathematicae Universitatis Carolinae 60.3 (2019): 351-360. <http://eudml.org/doc/294270>.

@article{Ghenciu2019,
abstract = {We investigate whether the projective tensor product of two Banach spaces $X$ and $Y$ has the reciprocal Dunford–Pettis property of order $p$, $1\le p<\infty $, when $X$ and $Y$ have the respective property.},
author = {Ghenciu, Ioana},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {reciprocal Dunford--Pettis property; spaces of compact operators},
language = {eng},
number = {3},
pages = {351-360},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The reciprocal Dunford–Pettis property of order $p$ in projective tensor products},
url = {http://eudml.org/doc/294270},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Ghenciu, Ioana
TI - The reciprocal Dunford–Pettis property of order $p$ in projective tensor products
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 3
SP - 351
EP - 360
AB - We investigate whether the projective tensor product of two Banach spaces $X$ and $Y$ has the reciprocal Dunford–Pettis property of order $p$, $1\le p<\infty $, when $X$ and $Y$ have the respective property.
LA - eng
KW - reciprocal Dunford--Pettis property; spaces of compact operators
UR - http://eudml.org/doc/294270
ER -

References

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  1. Albiac F., Kalton N. J., Topics in Banach Space Theory, Graduate Texts in Mathematics, 233, Springer, New York, 2006. Zbl1094.46002MR2192298
  2. Bator E. M., Lewis P. W., 10.1002/mana.19921570109, Math. Nachr. 157 (1992), 99–103. Zbl0792.47021MR1233050DOI10.1002/mana.19921570109
  3. Bessaga C., Pełczyński A., 10.4064/sm-17-2-151-164, Studia Math. 17 (1958), 151–164. MR0115069DOI10.4064/sm-17-2-151-164
  4. Bourgain J., New classes of p -spaces, Lecture Notes in Mathematics, 889, Springer, Berlin, 1981. MR0639014
  5. Castillo J. M., Sanchez F., Dunford–Pettis-like properties of continuous vector function spaces, Rev. Mat. Univ. Complut. Madrid 6 (1993), no. 1, 43–59. MR1245024
  6. Diestel J., A survey of results related to the Dunford–Pettis property, Proc. of the Conf. on Integration, Topology, and Geometry in Linear Spaces, Contemp. Math., 2, Amer. Math. Soc., Provicence, 1980, pages 15–60. MR0621850
  7. Diestel J., Sequences and Series in Banach Spaces, Graduate Texts in Mathematics, 92, Springer, New York, 1984. MR0737004
  8. Diestel J., Jarchow H., Tonge A., Absolutely Summing Operators, Cambridge Studies in Advanced Mathematics, 43, Cambridge University Press, Cambridge, 1995. Zbl1139.47021MR1342297
  9. Diestel J., Uhl J. J. Jr., Vector Measures, Mathematical Surveys, 15, American Mathematical Society, Providence, 1977. Zbl0521.46035MR0453964
  10. Emmanuele G., A dual characterization of Banach spaces not containing 1 , Bull. Polish Acad. Sci. Math. 34 (1986), no. 3–4, 155–160. MR0861172
  11. Emmanuele G., Dominated operators on C [ 0 , 1 ] and the ( C R P ) , Collect. Math. 41 (1990), no. 1, 21–25. MR1134442
  12. Emmanuele G., 10.1017/S0305004100069632, Math. Proc. Cambridge Philos. Soc. 109 (1991), no. 1, 161–166. MR1075128DOI10.1017/S0305004100069632
  13. Emmanuele G., 10.1017/S0305004100075435, Math. Proc. Cambridge Philos. Soc. 111 (1992), no. 2, 331–335. MR1142753DOI10.1017/S0305004100075435
  14. Emmanuele G., Hensgen W., Property ( V ) of Pelczyński in projective tensor products, Proc. Roy. Irish Acad. Sect. A 95 (1995), no. 2, 227–231. MR1660381
  15. Emmanuele G., John K., 10.1023/A:1022483919972, Czechoslovak Math. J. 47 (1997), no. 1, 19–31. Zbl0903.46006MR1435603DOI10.1023/A:1022483919972
  16. Ghenciu I., Property ( w L ) and the reciprocal Dunford–Pettis property in projective tensor products, Comment. Math. Univ. Carolin. 56 (2015), no. 3, 319–329. MR3390279
  17. Ghenciu I., 10.2989/16073606.2017.1402383, Quaest. Math. 41 (2018), no. 6, 811–828. MR3857131DOI10.2989/16073606.2017.1402383
  18. Ghenciu I., 10.1007/s10474-018-0836-5, Acta Math. Hungar. 155 (2018), 439–457. MR3831309DOI10.1007/s10474-018-0836-5
  19. Ghenciu I., Lewis P., 10.4064/cm106-2-11, Colloq. Math. 106 (2006), no. 2, 311–324. MR2283818DOI10.4064/cm106-2-11
  20. Ghenciu I., Lewis P., 10.4064/ba56-3-7, Bull. Pol. Acad. Sci. Math. 56 (2008), no. 3–4, 239–256. Zbl1167.46016MR2481977DOI10.4064/ba56-3-7
  21. Pełczyński A., Banach spaces on which every unconditionally converging operator is weakly compact, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 641–648. Zbl0107.32504MR0149295
  22. Pełczyński A., 10.4064/sm-30-2-231-246, Studia Math. 30 (1968), 231–246. MR0232195DOI10.4064/sm-30-2-231-246
  23. Pełczyński A., Semadeni Z., 10.4064/sm-18-2-211-222, Studia Math. 18 (1959), 211–222. MR0107806DOI10.4064/sm-18-2-211-222
  24. Pitt H. R., 10.1112/jlms/s1-11.3.174, J. London Math. Soc. 11 (1936), no. 3, 174–180. Zbl0014.31201MR1574344DOI10.1112/jlms/s1-11.3.174
  25. Rosenthal H., 10.2307/2373824, Amer. J. Math. 99 (1977), no. 2, 362–378. MR0438113DOI10.2307/2373824
  26. Ryan R. A., Introduction to Tensor Products of Banach Spaces, Springer Monographs in Mathematics, Springer, London, 2002. Zbl1090.46001MR1888309
  27. Wojtaszczyk P., Banach Spaces for Analysts, Cambridge Studies in Advanced Mathematics, 25, Cambridge University Press, Cambridge, 1991. MR1144277

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