The numerical index of the $L_{p}$ space
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- by Elmouloudi Ed-Dari and Mohamed Amine Khamsi PDF
- Proc. Amer. Math. Soc. 134 (2006), 2019-2025 Request permission
Abstract:
We give a partial answer to the problem of computing the numerical index of $L_{p}[0, 1]$ for $1<p<\infty$.References
- F. F. Bonsall and J. Duncan, Numerical ranges of operators on normed spaces and of elements of normed algebras, London Mathematical Society Lecture Note Series, vol. 2, Cambridge University Press, London-New York, 1971. MR 0288583, DOI 10.1017/CBO9781107359895
- F. F. Bonsall and J. Duncan, Numerical ranges. II, London Mathematical Society Lecture Note Series, No. 10, Cambridge University Press, New York-London, 1973. MR 0442682, DOI 10.1017/CBO9780511662515
- H. F. Bohnenblust and S. Karlin, Geometrical properties of the unit sphere of Banach algebras, Ann. of Math. (2) 62 (1955), 217–229. MR 71733, DOI 10.2307/1969676
- Bernard Beauzamy, Introduction to Banach spaces and their geometry, 2nd ed., North-Holland Mathematics Studies, vol. 68, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 86. MR 889253
- J. Duncan, C. M. McGregor, J. D. Pryce, and A. J. White, The numerical index of a normed space, J. London Math. Soc. (2) 2 (1970), 481–488. MR 264371, DOI 10.1112/jlms/2.Part_{3}.481
- E. Ed-dari, On the numerical index of Banach spaces, to appear.
- Catherine Finet, Miguel Martín, and Rafael Payá, Numerical index and renorming, Proc. Amer. Math. Soc. 131 (2003), no. 3, 871–877. MR 1937425, DOI 10.1090/S0002-9939-02-06576-0
- B. W. Glickfeld, On an inequality of Banach algebra geometry and semi-inner product space theory, Illinois J. Math. 14 (1970), 76–81. MR 253024, DOI 10.1215/ijm/1256053302
- Karl E. Gustafson and Duggirala K. M. Rao, Numerical range, Universitext, Springer-Verlag, New York, 1997. The field of values of linear operators and matrices. MR 1417493, DOI 10.1007/978-1-4613-8498-4
- G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 (1961), 29–43. MR 133024, DOI 10.1090/S0002-9947-1961-0133024-2
- Ginés López, Miguel Martín, and Rafael Payá, Real Banach spaces with numerical index 1, Bull. London Math. Soc. 31 (1999), no. 2, 207–212. MR 1664125, DOI 10.1112/S002460939800513X
- Miguel Martín, A survey on the numerical index of a Banach space, Extracta Math. 15 (2000), no. 2, 265–276. III Congress on Banach Spaces (Jarandilla de la Vera, 1998). MR 1823892
- Miguel Martín and Rafael Payá, Numerical index of vector-valued function spaces, Studia Math. 142 (2000), no. 3, 269–280. MR 1792610, DOI 10.4064/sm-142-3-269-280
Additional Information
- Elmouloudi Ed-Dari
- Affiliation: Faculté des Sciences Jean Perrin, Université D’Artois, SP 18, 62307-Lens Cedex, France
- Email: Elmouloudi.Eddari@euler.univ.artois.fr
- Mohamed Amine Khamsi
- Affiliation: Department of Mathematical Sciences, University of Texas at El Paso, 500 West University Avenue, El Paso, Texas 79968-0514
- Email: mohamed@math.utep.edu
- Received by editor(s): October 14, 2004
- Received by editor(s) in revised form: February 10, 2005
- Published electronically: December 19, 2005
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 2019-2025
- MSC (2000): Primary 46B20, 47A12
- DOI: https://doi.org/10.1090/S0002-9939-05-08231-6
- MathSciNet review: 2215771