Title:
|
The reciprocal Dunford--Pettis property of order $p$ in projective tensor products (English) |
Author:
|
Ghenciu, Ioana |
Language:
|
English |
Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
ISSN:
|
0010-2628 (print) |
ISSN:
|
1213-7243 (online) |
Volume:
|
60 |
Issue:
|
3 |
Year:
|
2019 |
Pages:
|
351-360 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
We investigate whether the projective tensor product of two Banach spaces $X$ and $Y$ has the reciprocal Dunford--Pettis property of order $p$, $1\le\allowbreak p<\infty$, when $X$ and $Y$ have the respective property. (English) |
Keyword:
|
reciprocal Dunford--Pettis property |
Keyword:
|
spaces of compact operators |
MSC:
|
28B05 |
MSC:
|
46B20 |
MSC:
|
46B28 |
idZBL:
|
Zbl 07144899 |
idMR:
|
MR4034437 |
DOI:
|
10.14712/1213-7243.2019.014 |
. |
Date available:
|
2019-10-29T12:58:28Z |
Last updated:
|
2021-10-04 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147859 |
. |
Reference:
|
[1] Albiac F., Kalton N. J.: Topics in Banach Space Theory.Graduate Texts in Mathematics, 233, Springer, New York, 2006. Zbl 1094.46002, MR 2192298 |
Reference:
|
[2] Bator E. M., Lewis P. W.: Operators having weakly precompact adjoints.Math. Nachr. 157 (1992), 99–103. Zbl 0792.47021, MR 1233050, 10.1002/mana.19921570109 |
Reference:
|
[3] Bessaga C., Pełczyński A.: On bases and unconditional convergence of series in Banach spaces.Studia Math. 17 (1958), 151–164. MR 0115069, 10.4064/sm-17-2-151-164 |
Reference:
|
[4] Bourgain J.: New classes of $\mathcal{L}^p$-spaces.Lecture Notes in Mathematics, 889, Springer, Berlin, 1981. MR 0639014 |
Reference:
|
[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. MR 1245024 |
Reference:
|
[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. MR 0621850 |
Reference:
|
[7] Diestel J.: Sequences and Series in Banach Spaces.Graduate Texts in Mathematics, 92, Springer, New York, 1984. MR 0737004 |
Reference:
|
[8] Diestel J., Jarchow H., Tonge A.: Absolutely Summing Operators.Cambridge Studies in Advanced Mathematics, 43, Cambridge University Press, Cambridge, 1995. Zbl 1139.47021, MR 1342297 |
Reference:
|
[9] Diestel J., Uhl J. J. Jr.: Vector Measures.Mathematical Surveys, 15, American Mathematical Society, Providence, 1977. Zbl 0521.46035, MR 0453964 |
Reference:
|
[10] Emmanuele G.: A dual characterization of Banach spaces not containing $\ell^1$.Bull. Polish Acad. Sci. Math. 34 (1986), no. 3–4, 155–160. MR 0861172 |
Reference:
|
[11] Emmanuele G.: Dominated operators on $C[0,1]$ and the $( CRP)$.Collect. Math. 41 (1990), no. 1, 21–25. MR 1134442 |
Reference:
|
[12] Emmanuele G.: On the reciprocal Dunford–Pettis property and projective tensor products.Math. Proc. Cambridge Philos. Soc. 109 (1991), no. 1, 161–166. MR 1075128, 10.1017/S0305004100069632 |
Reference:
|
[13] Emmanuele G.: A remark on the containment of $c_0$ in spaces of compact operators.Math. Proc. Cambridge Philos. Soc. 111 (1992), no. 2, 331–335. MR 1142753, 10.1017/S0305004100075435 |
Reference:
|
[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. MR 1660381 |
Reference:
|
[15] Emmanuele G., John K.: Uncomplementability of spaces of compact operators in larger spaces of operators.Czechoslovak Math. J. 47 (1997), no. 1, 19–31. Zbl 0903.46006, MR 1435603, 10.1023/A:1022483919972 |
Reference:
|
[16] Ghenciu I.: Property $(wL)$ and the reciprocal Dunford–Pettis property in projective tensor products.Comment. Math. Univ. Carolin. 56 (2015), no. 3, 319–329. MR 3390279 |
Reference:
|
[17] Ghenciu I.: Dunford–Pettis like properties on tensor products.Quaest. Math. 41 (2018), no. 6, 811–828. MR 3857131, 10.2989/16073606.2017.1402383 |
Reference:
|
[18] Ghenciu I.: The $p$-Gelfand–Phillips property in spaces of operators and Dunford–Pettis like sets.Acta Math. Hungar. 155 (2018), 439–457. MR 3831309, 10.1007/s10474-018-0836-5 |
Reference:
|
[19] Ghenciu I., Lewis P.: The Dunford–Pettis property, the Gelfand-Phillips property, and $L$-sets.Colloq. Math. 106 (2006), no. 2, 311–324. MR 2283818, 10.4064/cm106-2-11 |
Reference:
|
[20] Ghenciu I., Lewis P.: The embeddability of $c_0$ in spaces of operators.Bull. Pol. Acad. Sci. Math. 56 (2008), no. 3–4, 239–256. Zbl 1167.46016, MR 2481977, 10.4064/ba56-3-7 |
Reference:
|
[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. Zbl 0107.32504, MR 0149295 |
Reference:
|
[22] Pełczyński A.: On Banach spaces containing $L_1(\mu)$.Studia Math. 30 (1968), 231–246. MR 0232195, 10.4064/sm-30-2-231-246 |
Reference:
|
[23] Pełczyński A., Semadeni Z.: Spaces of continuous functions (III). Spaces $C(\Omega)$ for $\Omega$ without perfect subsets.Studia Math. 18 (1959), 211–222. MR 0107806, 10.4064/sm-18-2-211-222 |
Reference:
|
[24] Pitt H. R.: A note on bilinear forms.J. London Math. Soc. 11 (1936), no. 3, 174–180. Zbl 0014.31201, MR 1574344, 10.1112/jlms/s1-11.3.174 |
Reference:
|
[25] Rosenthal H.: Point-wise compact subsets of the first Baire class.Amer. J. Math. 99 (1977), no. 2, 362–378. MR 0438113, 10.2307/2373824 |
Reference:
|
[26] Ryan R. A.: Introduction to Tensor Products of Banach Spaces.Springer Monographs in Mathematics, Springer, London, 2002. Zbl 1090.46001, MR 1888309 |
Reference:
|
[27] Wojtaszczyk P.: Banach Spaces for Analysts.Cambridge Studies in Advanced Mathematics, 25, Cambridge University Press, Cambridge, 1991. MR 1144277 |
. |