Limited p -converging operators and relation with some geometric properties of Banach spaces

Mohammad B. Dehghani; Seyed M. Moshtaghioun

Commentationes Mathematicae Universitatis Carolinae (2021)

  • Volume: 62, Issue: 4, page 417-430
  • ISSN: 0010-2628

Abstract

top
By using the concepts of limited p -converging operators between two Banach spaces X and Y , L p -sets and L p -limited sets in Banach spaces, we obtain some characterizations of these concepts relative to some well-known geometric properties of Banach spaces, such as * -Dunford–Pettis property of order p and Pelczyński’s property of order p , 1 ≤ p < ∞ .

How to cite

top

Dehghani, Mohammad B., and Moshtaghioun, Seyed M.. "Limited $p$-converging operators and relation with some geometric properties of Banach spaces." Commentationes Mathematicae Universitatis Carolinae 62.4 (2021): 417-430. <http://eudml.org/doc/298254>.

@article{Dehghani2021,
abstract = {By using the concepts of limited $p$-converging operators between two Banach spaces $X$ and $Y$, $L_p$-sets and $L_p$-limited sets in Banach spaces, we obtain some characterizations of these concepts relative to some well-known geometric properties of Banach spaces, such as $*$-Dunford–Pettis property of order $p$ and Pelczyński’s property of order $p$, $1\le p<\infty $.},
author = {Dehghani, Mohammad B., Moshtaghioun, Seyed M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Gelfand–Phillips property; Schur property; $p$-Schur property; weakly $p$-compact set; reciprocal Dunford–Pettis property of order $p$},
language = {eng},
number = {4},
pages = {417-430},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Limited $p$-converging operators and relation with some geometric properties of Banach spaces},
url = {http://eudml.org/doc/298254},
volume = {62},
year = {2021},
}

TY - JOUR
AU - Dehghani, Mohammad B.
AU - Moshtaghioun, Seyed M.
TI - Limited $p$-converging operators and relation with some geometric properties of Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2021
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62
IS - 4
SP - 417
EP - 430
AB - By using the concepts of limited $p$-converging operators between two Banach spaces $X$ and $Y$, $L_p$-sets and $L_p$-limited sets in Banach spaces, we obtain some characterizations of these concepts relative to some well-known geometric properties of Banach spaces, such as $*$-Dunford–Pettis property of order $p$ and Pelczyński’s property of order $p$, $1\le p<\infty $.
LA - eng
KW - Gelfand–Phillips property; Schur property; $p$-Schur property; weakly $p$-compact set; reciprocal Dunford–Pettis property of order $p$
UR - http://eudml.org/doc/298254
ER -

References

top
  1. Albiac F., Kalton N. J., Topics in Banach Space Theory, Graduate Texts in Mathematics, 233, Springer, New York, 2006. Zbl1094.46002MR2192298
  2. Bourgain J., Diestel J., 10.1002/mana.19841190105, Math. Nachr. 119 (1984), 55–58. Zbl0601.47019MR0774176DOI10.1002/mana.19841190105
  3. 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
  4. Castillo J. M. F., Sánchez F., 10.1006/jmaa.1994.1246, J. Math. Anal. Appl. 185 (1994), no. 2, 256–261. MR1283055DOI10.1006/jmaa.1994.1246
  5. Defant A., Floret K., Tensor Norms and Operator Ideals, North-Holland Mathematics Studies, 176, North-Holland Publishing, Amsterdam, 1993. MR1209438
  6. Dehghani M. B., Moshtaghioun S. M., 10.1215/20088752-2017-0033, Ann. Funct. Anal. 9 (2018), no. 1, 123–136. MR3758748DOI10.1215/20088752-2017-0033
  7. Dehghani M. B., Moshtaghioun S. M., Dehghani M., On the limited p -Schur property of some operator spaces, Int. J. Anal. Appl. 16 (2018), no. 1, 50–61. MR3758748
  8. 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
  9. Delgado J. M., Piñeiro C., 10.1016/j.jmaa.2013.08.045, J. Math. Anal. Appl. 410 (2014), no. 2, 713–718. MR3111861DOI10.1016/j.jmaa.2013.08.045
  10. Diestel J., Jarchow H., Tonge A., Absolutely summing operators, Cambridge Studies in Advanced Mathematics, 43, Cambridge University Press, Cambridge, 1995. MR1342297
  11. Drewnowski L., 10.1007/BF01229808, Math. Z. 193 (1986), no. 3, 405–411. MR0862887DOI10.1007/BF01229808
  12. Emmanuele G., A dual characterization of Banach spaces not containing ℓ 1 , Bull. Polish Acad. Sci. Math. 34 (1986), no. 3–4, 155–160. MR0861172
  13. Fourie J. H., Zeekoei E. D., 10.2989/16073606.2013.779611, Quaest. Math. 37 (2014), no. 3, 349–358. MR3285289DOI10.2989/16073606.2013.779611
  14. Fourie J. H., Zeekoei E. D., 10.2989/16073606.2017.1301591, Quaest. Math. 40 (2017), no. 5, 563–579. MR3691468DOI10.2989/16073606.2017.1301591
  15. Ghenciu I., Lewis P., 10.4064/cm106-2-11, Colloq. Math. 106 (2006), no. 2, 311–324. MR2283818DOI10.4064/cm106-2-11
  16. Grothendieck A., 10.4153/CJM-1953-017-4, Canad. J. Math. 5 (1953), 129–173 (French). Zbl0050.10902MR0058866DOI10.4153/CJM-1953-017-4
  17. Karn A. K., Sinha D. P., 10.1017/S0017089513000360, Glasg. Math. J. 56 (2014), no. 2, 427–437. MR3187909DOI10.1017/S0017089513000360
  18. Li L., Chen D., Chávez-Domínguez J. A., 10.1002/mana.201600335, Math. Nachr. 291 (2018), no. 2–3, 420–442. MR3767145DOI10.1002/mana.201600335
  19. Moshtaghioun S. M., Zafarani J., 10.11650/twjm/1500403855, Taiwanese J. Math. 10 (2006), no. 3, 691–698. MR2206322DOI10.11650/twjm/1500403855
  20. Pelczyński 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. MR0149295
  21. Ruess W., 10.1016/S0304-0208(08)71467-1, Functional Analysis: Surveys and Recent Results III, Paderborn, 1983, North-Holland Math. Stud., 90, Notas Mat., 94, North-Holland, Amsterdam, 1984, pages 59–78. Zbl0573.46007MR0761373DOI10.1016/S0304-0208(08)71467-1
  22. Ryan R. A., Introduction to Tensor Products of Banach Spaces, Springer Monographs in Mathematics, Springer, London, 2002. Zbl1090.46001MR1888309
  23. Salimi M., Moshtaghioun S. M., 10.15352/bjma/1313363004, Banach J. Math. Anal. 5 (2011), no. 2, 84–92. MR2792501DOI10.15352/bjma/1313363004
  24. Schlumprecht T., Limited sets in injective tensor products, Functional Analysis, Austin, 1987/1989, Lecture Notes in Math., 1470, Longhorn Notes, Springer, Berlin, 1991, pages 133–158. MR1126743

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.