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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new proof of proximinality for $ M$-ideals


Authors: V. Indumathi and S. Lalithambigai
Journal: Proc. Amer. Math. Soc. 135 (2007), 1159-1162
MSC (2000): Primary 46B20, 41A50, 41A65
Published electronically: October 11, 2006
MathSciNet review: 2262920
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Abstract: We give a new and a simple proof of proximinality for $ M$-ideals. Unlike the known proofs, our proof derives proximinality of $ M$-ideals directly from the definition of an $ M$-ideal, using the Bishop-Phelps theorem.


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Additional Information

V. Indumathi
Affiliation: Department of Mathematics, Pondicherry University, Kalapet, Pondicherry–605014, India
Email: pdyindumath@gmail.com

S. Lalithambigai
Affiliation: Department of Mathematics, Pondicherry University, Kalapet, Pondicherry–605014, India
Email: s_lalithambigai@yahoo.co.in

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08701-6
PII: S 0002-9939(06)08701-6
Keywords: Proximinal subspace, $M$-ideal.
Received by editor(s): November 14, 2005
Published electronically: October 11, 2006
Additional Notes: The first author was partially supported by DST-NSF project No. DST/INT/US(NSF-RPO-0141)/2003
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2006 American Mathematical Society