Pacific Journal of Mathematics

Dentability, trees, and Dunford-Pettis operators on $L_1$.

Maria Girardi

Article information

Source
Pacific J. Math., Volume 148, Number 1 (1991), 59-79.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102644782

Mathematical Reviews number (MathSciNet)
MR1091530

Zentralblatt MATH identifier
0718.46007

Subjects
Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46B22: Radon-Nikodým, Kreĭn-Milman and related properties [See also 46G10] 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22] 47D15

Citation

Girardi, Maria. Dentability, trees, and Dunford-Pettis operators on $L_1$. Pacific J. Math. 148 (1991), no. 1, 59--79. https://projecteuclid.org/euclid.pjm/1102644782


Export citation

References

  • [Bl] J. Bourgain, On martingales in conjugate Banachspaces,unpublished.
  • [B2] J. Bourgain, Dunford-Pettis operators on L\ and the Radon-Nikodym property, Israel J. Math., 37 (1980), 34-47.
  • [B3] J. Bourgain, Sets with the Radon-Nikodymproperty in conjugate Banachspace, Studia Math., 66 (1980), 291-297.
  • [BR] J. Bourgain and H. P. Rosenthal, Martingales valued in certainsubspaces of U , Israel J. Math., 37 (1980), 54-75.
  • [DU] J. Diestel and J. J. Uhl, Jr., Vector Measures,Math. Surveys, no. 15,Amer. Math. Soc,Providence, R.I., 1977.
  • [DU] J. Diestel and J. J. Uhl, Progressin VectorMeasures 1977-1983, Measuretheory and itsap- plications (Sherbrooke,Que., 1982), Lecture Notes in Math., vol. 1033, Springer-Verlag, Berlin and New York, 1983,pp. 144-192.
  • [GGMS] N. Ghoussoub, G. Godefroy, B. Maurey, and W. Schachermayer, Some topologicalandgeometricalstructuresin Banachspaces,Mem.Amer.Math. Soc, vol. 70, no. 378,Amer. Math. Soc,Providence, R.I., 1987.
  • [G] Maria Girardi, Compactness in L\, Dunford-Pettis operators, geometry of Banachspaces (to appear in Proc Amer. Math.Soc.)
  • [GU] Maria Girardi and J. J. Uhl, Jr., Slices,RNP,strong regularity,andmar- tingales, Bull. Austral. Math. Soc,41, no. 3 (June 1990).
  • [J] Robert C. James, A separablesomewhat reflexive Banach space with non- separabledual, Bull. Amer. Math. Soc,80 (1974), 738-743.
  • [KR] Ken Kunen and Haskell Rosenthal, Martingaleproofs of somegeometrical results in Banachspace theory,Pacific J. Math., 100 (1982), 153-175.
  • [PU] Minos Petrakis and J. J. Uhl, Jr., Differentiation in Banach spaces, Pro- ceedings of the Analysis conference (Singapore 1986),North-Holland, New York, 1988.
  • [RU] L. H. Riddle and J. J. Uhl, Jr., Martingales and the fine line between As- plund spaces and spaces not containing a copy of l\, Martingale Theory in Harmonic Analysis and Banach Spaces,Lecture Notes in Mathematics, vol. 339, Springer-Verlag, Berlin and New York, 1981,pp. 145-156.
  • [R] Haskell Rosenthal, On the structureof non-dentable closed boundedconvex sets, Advances in Math., to appear.
  • [S] Charles Stegall, The Radon-Nikodym property in conjugate Banach spaces, Trans. Amer. Math. So, 206 (1975), 213-223.
  • [Tl] M. Talagrand, Petts integral and measure theory,Mem. Amer. Math. Soc, vol. 51, no. 307, Amer. Math. Soc, Providence, R.I., 1984.
  • [T2] M. Talagrand,A conjectureon convolution operatorsand a non-Dunford-Pettis oper- ator on L\, preprint.
  • [W] Alan Wessel, Some resultson Dunford-Pettis operators, strong regularityand the Radon-Nikodym property, Seminaire d'Analyse Fonctionnelle (Paris VII-VI, 1985-1986), Publications Mathematiques de Universite Paris VII, Paris.

See also

  • Errata : Maria Girardi, Zhibao Hu. Errata: ``Dentability, trees, and Dunford-Pettis operators on $L_1$''. Pacific Journal of Mathematics volume 157, issue 2, (1993), pp. 389-394.