L -limited-like properties on Banach spaces

Ioana Ghenciu

Commentationes Mathematicae Universitatis Carolinae (2023)

  • Volume: 64, Issue: 4, page 439-457
  • ISSN: 0010-2628

Abstract

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We study weakly precompact sets and operators. We show that an operator is weakly precompact if and only if its adjoint is pseudo weakly compact. We study Banach spaces with the p - L -limited * and the p -(SR * ) properties and characterize these classes of Banach spaces in terms of p - L -limited * and p -Right * subsets. The p - L -limited * property is studied in some spaces of operators.

How to cite

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Ghenciu, Ioana. "$L$-limited-like properties on Banach spaces." Commentationes Mathematicae Universitatis Carolinae 64.4 (2023): 439-457. <http://eudml.org/doc/299320>.

@article{Ghenciu2023,
abstract = {We study weakly precompact sets and operators. We show that an operator is weakly precompact if and only if its adjoint is pseudo weakly compact. We study Banach spaces with the $p$-$L$-limited$^*$ and the $p$-(SR$^*$) properties and characterize these classes of Banach spaces in terms of $p$-$L$-limited$^*$ and $p$-Right$^*$ subsets. The $p$-$L$-limited$^*$ property is studied in some spaces of operators.},
author = {Ghenciu, Ioana},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$p$-Right$^*$ set; Right$^*$ set; DP $p$-convergent operator; weakly precompact operator; limited $p$-convergent operator},
language = {eng},
number = {4},
pages = {439-457},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$L$-limited-like properties on Banach spaces},
url = {http://eudml.org/doc/299320},
volume = {64},
year = {2023},
}

TY - JOUR
AU - Ghenciu, Ioana
TI - $L$-limited-like properties on Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2023
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 64
IS - 4
SP - 439
EP - 457
AB - We study weakly precompact sets and operators. We show that an operator is weakly precompact if and only if its adjoint is pseudo weakly compact. We study Banach spaces with the $p$-$L$-limited$^*$ and the $p$-(SR$^*$) properties and characterize these classes of Banach spaces in terms of $p$-$L$-limited$^*$ and $p$-Right$^*$ subsets. The $p$-$L$-limited$^*$ property is studied in some spaces of operators.
LA - eng
KW - $p$-Right$^*$ set; Right$^*$ set; DP $p$-convergent operator; weakly precompact operator; limited $p$-convergent operator
UR - http://eudml.org/doc/299320
ER -

References

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  1. Alikhani M., 10.2298/FIL1914461A, Filomat 33 (2019), no. 14, 4461–4474. MR4049162DOI10.2298/FIL1914461A
  2. Andrews K. T., 10.1007/BF01406706, Math. Ann. 241 (1979), no. 1, 35–41. MR0531148DOI10.1007/BF01406706
  3. Bator E., Lewis P., Ochoa J., 10.4064/cm-78-1-1-17, Colloq. Math. 78 (1998), no. 1, 1–17. Zbl0948.46008MR1658115DOI10.4064/cm-78-1-1-17
  4. Bourgain J., Delbaen F., 10.1007/BF02414188, Acta Math. 145 (1980), no. 3–4, 155–176. MR0590288DOI10.1007/BF02414188
  5. Bourgain J., Diestel J., 10.1002/mana.19841190105, Math. Nachr. 119 (1984), 55–58. Zbl0601.47019MR0774176DOI10.1002/mana.19841190105
  6. Carrión H., Galindo P., Lourenço M., 10.4064/sm184-3-1, Studia Math. 184 (2008), no. 3, 205–216. MR2369139DOI10.4064/sm184-3-1
  7. Castillo J. M. F., Sanchez F., Dunford–Pettis like properties of continuous vector function spaces, Rev. Mat. Univ. Complut. Madrid 6 (1993), no. 1, 43–59. MR1245024
  8. Cembranos P., C ( K , E ) contains a complemented copy of c 0 , Proc. Amer. Math. Soc. 91 (1984), no. 4, 556–558. MR0746089
  9. Cilia R., Emmanuele G., 10.4064/cm6184-12-2015, Colloq. Math. 146 (2017), no. 2, 239–252. MR3622375DOI10.4064/cm6184-12-2015
  10. Dehghani M., Dehghani M. B., Moshtaghioun M. S., Sequentially right Banach spaces of order p , Comment. Math. Univ. Carolin. 61 (2020), no. 1, 51–67. MR4093429
  11. Diestel J., A survey of results related to the Dunford–Pettis property, Proc. of Conf. on Integration, Topology, and Geometry in Linear Spaces, Univ. North Carolina, Chapel Hill, N.C., 1979, Contemp. Math., 2, Amer. Math. Soc., Providence, 1980, pages 15–60. MR0621850
  12. Diestel J., Jarchow H., Tonge A., Absolutely Summing Operators, Cambridge Studies in Advanced Mathematics, 43, Cambridge University Press, Cambridge, 1995. Zbl1139.47021MR1342297
  13. Drewnowski L., Emmanuele G., 10.1007/BF02850021, Rend. Circ. Mat. Palermo (2) 38 (1989), no. 3, 377–391. MR1053378DOI10.1007/BF02850021
  14. Emmanuele G., 10.1007/BF01190118, Arch. Math. (Basel) 58 (1992), no. 5, 477–485. MR1156580DOI10.1007/BF01190118
  15. Fourie J. H., Zeekoei E. D., 10.2989/16073606.2013.779611, Quaest. Math. 37 (2014), no. 3, 349–358. MR3285289DOI10.2989/16073606.2013.779611
  16. Fourie J. H., Zeekoei E. D., 10.2989/16073606.2017.1301591, Quaest. Math. 40 (2017), no. 5, 563–579. MR3691468DOI10.2989/16073606.2017.1301591
  17. Ghenciu I., 10.4064/cm138-2-10, Colloq. Math. 138 (2015), no. 2, 255–269. MR3312111DOI10.4064/cm138-2-10
  18. Ghenciu I., 10.1007/s00605-016-0884-2, Monatsh. Math. 181 (2016), no. 3, 609–628. MR3552802DOI10.1007/s00605-016-0884-2
  19. Ghenciu I., A note on some isomorphic properties in projective tensor products, Extracta Math. 32 (2017), no. 1, 1–24. MR3726522
  20. Ghenciu I., 10.1007/s10474-018-0836-5, Acta Math. Hungar. 155 (2018), no. 2, 439–457. MR3831309DOI10.1007/s10474-018-0836-5
  21. Ghenciu I., 10.15352/aot.1802-1318, Adv. Oper. Theory 4 (2019), no. 2, 369–387. MR3883141DOI10.15352/aot.1802-1318
  22. Ghenciu I., 10.1007/s00605-022-01738-6, Monatsh. Math. 200 (2023), no. 2, 255–270. MR4544297DOI10.1007/s00605-022-01738-6
  23. Ghenciu I., Lewis P., 10.4064/ba54-3-6, Bull. Pol. Acad. Sci. Math. 54 (2006), no. 3–4, 237–256. Zbl1118.46016MR2287199DOI10.4064/ba54-3-6
  24. Ghenciu I., Lewis P., 10.4064/cm126-2-7, Colloq. Math. 126 (2012), no. 2, 231–256. Zbl1256.46009MR2924252DOI10.4064/cm126-2-7
  25. Ghenciu I., Popescu R., 10.2989/16073606.2023.2182243, Quaest. Math. 47 (2024), no. 1, 21–42. MR4713267DOI10.2989/16073606.2023.2182243
  26. Kačena M., On sequentially right Banach spaces, Extracta Math. 26 (2011), no. 1, 1–27. MR2908388
  27. Karn A. K., Sinha D. P., 10.1017/S0017089513000360, Glasg. Math. J. 56 (2014), no. 2, 427–437. MR3187909DOI10.1017/S0017089513000360
  28. Li L., Chen D., Chavez-Dominguez J. A., 10.1002/mana.201600335, Math. Nachr. 291 (2018), no. 2–3, 420–442. MR3767145DOI10.1002/mana.201600335
  29. 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
  30. Peralta A. M., Villanueva I., Wright J. D. M., Ylinen K., 10.1016/j.jmaa.2006.02.066, J. Math. Anal. Appl. 325 (2007), no. 2, 968–974. MR2270063DOI10.1016/j.jmaa.2006.02.066
  31. Rosenthal H. P., 10.2307/2373824, Amer. J. Math. 99 (1977), no. 2, 362–378. MR0438113DOI10.2307/2373824
  32. Salimi M., Moshtaghiun S. M., A new class of Banach spaces and its relation with some geometric properties of Banach spaces, Abstr. Appl. Anal. (2012), Art. ID 212957, 8 pages. MR2910729
  33. Wojtaszczyk P., Banach Spaces for Analysts, Cambridge Studies in Advanced Mathematics, 25, Cambridge University Press, Cambridge, 1991. MR1144277

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