On Ball Dentable Property in Banach Spaces

  • Sudeshna BasuEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 302)


In this work, we introduce the notion of Ball dentable property in Banach spaces. We study certain stability results for the \(w^*\)-Ball dentable property leading to a discussion on Ball rentability in the context of ideals of Banach spaces. We prove that the \(w^*\)-Ball-dentable property can be lifted from an M-ideal to the whole Banach Space. We also prove similar results for strict ideals of a Banach space. We note that the space \(C(K,X)^*\) has \(w^*\)-Ball dentable property when K is dispersed and \(X^*\) has the \(w^*\)-Ball dentable property.


Slices M-Ideals Strict ideals 


46B20 46B28 


  1. 1.
    Acosta, A.D., Kaminska, A., Mastylo, M.: The Daugavet property in rearrangement invariant spaces. Trans. Am. Math. Soc. 367, 4061–4078 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Basu, S., Rao, T.S.S.R.K.: On small combination of slices in banach spaces. Extr. Math. 31, 1–10 (2016)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Bourgin, R.D.: Geometric aspects of convex sets with the Radon-Nikodm property. Lecture Notes in Mathematics, vol. 993, p. xii+ 474. Springer, Berlin (1983)CrossRefGoogle Scholar
  4. 4.
    Godefroy, G., Kalton, N.J., Saphar, P.D.: Unconditional ideals in Banach spaces. Studia Math. 104, 13–59 (1993)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Harmand, P., Werner, D., Werner, W.: \(M\)-Ideals in Banach Spaces and Banach Algebras. Lecture Notes in Mathematics, vol. 1547. Springer, Berlin (1993)CrossRefGoogle Scholar
  6. 6.
    Lacey, H.E.: The Isometric Theory of Classical Banach Spaces. Die Grundlehren der mathematischen Wissenschaften, Band, vol. 208, pp. x+270 . Springer, New York (1974)CrossRefGoogle Scholar
  7. 7.
    Lin, B.L., Lin, P.K., Troyanski, S.: Charecterisation of denting points. Proc. Am. Math. Soc. 102, 526–528 (1988)CrossRefGoogle Scholar
  8. 8.
    Oja, E.: On \(M\)-ideals of compact operators in Lorentz sequence spaces. J. Math. Anal. Appl. 259, 439–452 (2001)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Rao, T.S.S.R.K. : On ideals in Banach spaces. Rocky Mt. J. Math. 31, 595-609 (2001)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Rosenthal, H.P.: On the structure of non-dentable closed bounded convex sets. Adv. Math. 70, 1–58 (1988)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsGeorge Washington UniversityWashington DCUSA

Personalised recommendations