Skip to main content
SpringerLink
Log in

On some classes of Dunford–Pettis-like operators

  • Published:
Rendiconti del Circolo Matematico di Palermo Series 2 Aims and scope Submit manuscript

Abstract

In this paper we give characterizations of weak Dunford–Pettis, \(\hbox {weak}^*\) Dunford–Pettis, weak p-convergent, and \(\hbox {weak}^*\)p-convergent operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aliprantis, C.D., Burknishaw, O.: Positive Operators. Springer, Dordrecht (2006). (Reprint of the 1985 original copy)

    Book  Google Scholar 

  2. Andrews, K.: Dunford–Pettis sets in the space of Bochner integrable functions. Math. Ann. 241, 35–41 (1979)

    Article  MathSciNet  Google Scholar 

  3. Bourgain, J., Diestel, J.: Limited operators and strict cosingularity. Math. Nachr. 119, 55–58 (1984)

    Article  MathSciNet  Google Scholar 

  4. Borwein, J., Fabian, M., Vanderweff, J.: Characterizations of Banach spaces via convex and other locally Lipschitz functions. Acta Math. Vietnam 22, 53–69 (1997)

    MathSciNet  MATH  Google Scholar 

  5. Carrión, H., Galindo, P., Lourenço, M.L.: A stronger Dunford–Pettis property. Studia Math. 3, 205–216 (2008). (Lourenço)

    Article  MathSciNet  Google Scholar 

  6. Castillo, J., Sánchez, F.: Dunford–Pettis like properties of continuous vector function spaces. Revista Mat. Univ. Complut. Madr. 6, 43–59 (1993)

    MathSciNet  MATH  Google Scholar 

  7. Diestel, J.: Sequences and Series in Banach Spaces, Graduate Texts in Mathematics, vol. 92. Springer, Berlin (1984)

    Book  Google Scholar 

  8. Diestel, J.: A survey of results related to the Dunford–Pettis property. Contemp. Math. 2, 15–60 (1980)

    Article  MathSciNet  Google Scholar 

  9. Diestel, J., Uhl Jr., J.J.: Vector Measures, Mathematical Surveys, vol. 15. American Mathematical Society, Providence (1977)

    Book  Google Scholar 

  10. Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators, Cambridge Studies in Advanced Mathematics, vol. 43. Cambridge University Press, Cambridge (1995)

    Book  Google Scholar 

  11. El Kaddouri, A., H’michane, J., Bouras, K., Moussa, M.: On the class of \(\text{ weak }^*\) Dunford-Pettis operators. Rend. Circ. Mat. Palermo 62(2), 261–265 (2013)

    Article  MathSciNet  Google Scholar 

  12. Emmanuele, G.: A dual characterization of Banach spaces not containing \(\ell ^1\). Bull. Pol. Acad. Sci. Math. 34, 155–160 (1986)

    MathSciNet  MATH  Google Scholar 

  13. Emmanuele, G.: Banach spaces in which Dunford–Pettis sets are relatively compact. Arch. Math. 58, 477–485 (1992)

    Article  MathSciNet  Google Scholar 

  14. Fourie, J.H., Zeekoei, E.D.: \(DP^*\)-properties of order \(p\) on Banach spaces. Quaest. Math. 37, 349–358 (2014)

    Article  MathSciNet  Google Scholar 

  15. Fourie, J.H., Zeekoei, E.D.: On weak-star-\(p\)-convergent operators. Quaest. Math. (2017). https://doi.org/10.2989/16073606.2017.1301591

    Article  MathSciNet  MATH  Google Scholar 

  16. Ghenciu, I., Lewis, P.: Completely continuous operators. Colloq. Math. 126(2), 231–256 (2012). https://doi.org/10.4064/cm126-2-7

    Article  MathSciNet  MATH  Google Scholar 

  17. Ghenciu, I.: Some classes of Banach spaces and complemented subspaces of operators. Adv. Oper. Theory (2018). https://doi.org/10.15352/aot.1802-1318. ISSN 2538-225X (electronic)

  18. Ghenciu, I.: Dunford–Pettis like properties on tensor products. Quaest. Math. 41, 811–828 (2018)

    Article  MathSciNet  Google Scholar 

  19. Ghenciu, I.: A note on Dunford–Pettis like properties and complemented spaces of operators. Comment. Math. Univ. Carolin. 59(2), 207–222 (2018)

    MathSciNet  MATH  Google Scholar 

  20. Ghenciu, I.: \(L\)-Sets and property \((SR^*)\) in spaces of compact operators. Monatsh. Math. 181(3), 609–628 (2016). https://doi.org/10.1007/s00605-016-0884-2

    Article  MathSciNet  MATH  Google Scholar 

  21. Jaramillo, J.A., Prieto, A., Zaldueno, I.: Sequential convergence and Dunford–Pettis properties. An. Acad. Sci. Fenn. 25, 467–475 (2000)

    MathSciNet  MATH  Google Scholar 

  22. Jinxi, C., Yongming, W.: Characterizations of Banach spaces with relatively compact Dunford–Pettis sets. Adv. Math. (China) (2016). https://doi.org/10.11845/sxjz.2014095b

    Article  MathSciNet  MATH  Google Scholar 

  23. Salimi, M., Moshtaghiun, M.: The Gelfand–Phillips property in closed subspaces of some operator spaces. Banach J. Math. Anal. 5, 84–92 (2011)

    Article  MathSciNet  Google Scholar 

  24. Schlumprecht, T.: Limited sets in Banach spaces. Ph.D. Dissertation, Ludwig-Maximilians-Universität, Munich (1987)

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, University of Wisconsin-River Falls, River Falls, WI, 54022, USA

    Ioana Ghenciu

Authors
  1. Ioana Ghenciu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ioana Ghenciu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghenciu, I. On some classes of Dunford–Pettis-like operators. Rend. Circ. Mat. Palermo, II. Ser 69, 1149–1163 (2020). https://doi.org/10.1007/s12215-019-00463-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12215-019-00463-8

Keywords

Mathematics Subject Classification

Search

Navigation