Characterization of Strong Ball Proximinality in L_1-Predual Spaces

C. R. Jayanarayanan

doi:10.68381/jca26027

Abstract

We characterize finite co-dimensional strongly ball proximinal subspaces of

L_1

-predual spaces and prove that they are precisely the finite co-dimensional strongly proximinal subspaces.

Author information

Contact details are reproduced from the original publication and may be historical.

C. R. Jayanarayanan

Dept. of Mathematics, Indian Institute of Technology, Palakkad 678557, India

crjayan@iitpkd.ac.in

Keywords

Strong proximinality
ball proximinality
strong ball proximinality
L1-predual spaces

Mathematics Subject Classification

41A65; 46B20, 41A50, 46E15

References

D. Amir, F. Deutsch: Suns, moons, and quasi-polyhedra, J. Approx. Theory 6 (1972) 176–201.https://doi.org/10.1016/0021-9045(72)90073-1 Google Scholar
P. Bandyopadhyay, B.-L. Lin, T. S. S. R. K. Rao: Ball proximinality in Banach spaces, in: Banach Spaces and Their Applications in Analysis, W. de Gruyter, Berlin (2007) 251–264.Google Scholar
E. Behrends: On the principle of local reflexivity, Studia Math. 100(2) (1991) 109–128.https://doi.org/10.4064/sm-100-2-109-128 Google Scholar
C. Franchetti, R. Payá: Banach spaces with strongly subdifferentiable norm, Boll. Un. Mat. Ital. B7(1) (1993) 45–70.Google Scholar
G. Godefroy, V. Indumathi: Strong proximinality and polyhedral spaces, Rev. Mat. Complut. 14(1) (2001) 105–125.https://doi.org/10.5209/rev_REMA.2001.v14.n1.17047 Google Scholar
C. R. Jayanarayanan, S. Lalithambigai: Strong ball proximinality and continuity of metric projection in L1 -predual spaces, J. Approx. Theory 213 (2017) 120–135.https://doi.org/10.1016/j.jat.2016.08.003 Google Scholar
C. R. Jayanarayanan, T. Paul: Strong proximinality and intersection properties of balls in Banach spaces, J. Math. Anal. Appl. 426(2) (2015) 1217–1231.https://doi.org/10.1016/j.jmaa.2015.01.013 Google Scholar
J. Lindenstrauss: Extension of Compact Operators, Mem. Amer. Math. Soc. 48, American Mathematical Society, Providence (1964).https://doi.org/10.1090/memo/0048 Google Scholar
F. B. Saidi: On the proximinality of the unit ball of proximinal subspaces in Banach spaces: a counterexample, Proc. Amer. Math. Soc. 133(9) (2005) 2697–2703.https://doi.org/10.1090/S0002-9939-05-08152-9 Google Scholar

Suggested citation

Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.

[1] D. Amir, F. Deutsch: Suns, moons, and quasi-polyhedra, J. Approx. Theory 6 (1972) 176–201.https://doi.org/10.1016/0021-9045(72)90073-1 Google Scholar

[2] P. Bandyopadhyay, B.-L. Lin, T. S. S. R. K. Rao: Ball proximinality in Banach spaces, in: Banach Spaces and Their Applications in Analysis, W. de Gruyter, Berlin (2007) 251–264.Google Scholar

[3] E. Behrends: On the principle of local reflexivity, Studia Math. 100(2) (1991) 109–128.https://doi.org/10.4064/sm-100-2-109-128 Google Scholar

[4] C. Franchetti, R. Payá: Banach spaces with strongly subdifferentiable norm, Boll. Un. Mat. Ital. B7(1) (1993) 45–70.Google Scholar

[5] G. Godefroy, V. Indumathi: Strong proximinality and polyhedral spaces, Rev. Mat. Complut. 14(1) (2001) 105–125.https://doi.org/10.5209/rev_REMA.2001.v14.n1.17047 Google Scholar

[6] C. R. Jayanarayanan, S. Lalithambigai: Strong ball proximinality and continuity of metric projection in L1 -predual spaces, J. Approx. Theory 213 (2017) 120–135.https://doi.org/10.1016/j.jat.2016.08.003 Google Scholar

[7] C. R. Jayanarayanan, T. Paul: Strong proximinality and intersection properties of balls in Banach spaces, J. Math. Anal. Appl. 426(2) (2015) 1217–1231.https://doi.org/10.1016/j.jmaa.2015.01.013 Google Scholar

[8] J. Lindenstrauss: Extension of Compact Operators, Mem. Amer. Math. Soc. 48, American Mathematical Society, Providence (1964).https://doi.org/10.1090/memo/0048 Google Scholar

[9] F. B. Saidi: On the proximinality of the unit ball of proximinal subspaces in Banach spaces: a counterexample, Proc. Amer. Math. Soc. 133(9) (2005) 2697–2703.https://doi.org/10.1090/S0002-9939-05-08152-9 Google Scholar