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Norm Attaining Bilinear Forms on Spaces of Continuous Functions

Published online by Cambridge University Press:  18 May 2009

J. Alaminos ,
Y. S. Choi ,
S. G. Kim  and
R. Payá
J. Alaminos
Affiliation:
Departamento De Análisis Matemático Facultad De Ciencias, Universidad De Granada, 18071 Granada Spain E-mail: alaminos@goliat.ugr.es and rpaya@goliat.ugr.es
Y. S. Choi
Affiliation:
Department of Mathematics pohang, University of Science and Technology, Pohang Korea E-mail: mathchoi@euclid.postech.ac.kr and skim@euclid.postech.ac.kr
S. G. Kim
Affiliation:
Department of Mathematics pohang, University of Science and Technology, Pohang Korea E-mail: mathchoi@euclid.postech.ac.kr and skim@euclid.postech.ac.kr
R. Payá
Affiliation:
Departamento De Análisis Matemático Facultad De Ciencias, Universidad De Granada, 18071 Granada Spain E-mail: alaminos@goliat.ugr.es and rpaya@goliat.ugr.es
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Abstract

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We show that continuous bilinear forms on spaces of continuous functions can be approximated by norm attaining bilinear forms.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 3 , September 1998 , pp. 359 - 365
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

REFERENCES

1.Acosta, M. D., Aguirre, F. J. and Paya, R., There is no bilinear Bishop-Phelps theorem, Israel J. Math. 93 (1996), 221–227.CrossRefGoogle Scholar
2.Aron, R. M., Finet, C. and Werner, E., Norm-attaining n-linear forms and the Radon-Nikodym property, in Proc. 2nd Conf. on Function Spaces (Jarosz, K., ed.), L. N. Pure and Appl. Math., Marcel Dekker (1995), pp. 19–28.Google Scholar
3.Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and of elements of normed algebras, London Math. Soc. Lect. Notes Ser. 2 (Cambridge Univ. Press, 1971).CrossRefGoogle Scholar
4.Bonsall, F. F. and Duncan, J., Numerical ranges II, London Math. Soc. Lect. Notes Ser. 10 (Cambridge Univ. Press, 1973).CrossRefGoogle Scholar
5.Choi, Y. S., Norm attaining bilinear forms on L1[0, 1], J. Math. Anal. Appl. 211 (1997), 295–300.CrossRefGoogle Scholar
6.Choi, Y. S. and Kim, S. G., Norm or numerical radius attaining multilinear mappings and polynomials, J. London Math. Soc. 54 (1996), 135–147.CrossRefGoogle Scholar
7.Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces, Pitman Monographs and Surveys in Pure and Appl. Math. 64 (Longman Sc. & Tech., Essex, 1993).Google Scholar
8.Diestel, J. and Uhl, J. J. Jr, Vector measures, Math. Surveys 15 (Amer. Math. Soc, Providence R.I. 1977).CrossRefGoogle Scholar
9.Emmanuele, G., A remark on the containment of Co in spaces of compact operators, Math. Proc. Camb. Phil. Soc. III (1992), 331–335.CrossRefGoogle Scholar
10.Finet, C. and Payá, R., Norm attaining operators from L1 into L∞ Israel J. Math, (to appear).Google Scholar
11.Grothendieck, A., Sur les applications lineaires faiblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1953), 129–173.CrossRefGoogle Scholar
12.Gutierrez, J. M., Weakly continuous functions on Banach spaces not containing lu Proc. Amer. Math. Soc. 1993 no. 1 (1993), 147–152.Google Scholar
13.Jiménez-Sevilla, M. and Payá, R., Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces, Studia Math. 127 (1998), 99–112.CrossRefGoogle Scholar
14.Kalton, N., Spaces of compact operators, Math. Ann. 208 (1974), 267–278.CrossRefGoogle Scholar
15.Lindenstrauss, J., On operators which attain their norm, Israel J. Math. 1 (1963), 139–148.CrossRefGoogle Scholar
16.Rudin, W., Real and complex analysis (McGraw-Hill, New York, 1966).Google Scholar
17.Schachermayer, W., Norm attaining operators on some classical Banach spaces, Pac. J. Math. 105, no. 2 (1983) 427–438.CrossRefGoogle Scholar