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Two-dimensional Banach spaces with polynomial numerical index zero. (English) Zbl 1213.46015
Summary: We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.
46B04Isometric theory of Banach spaces
46G25(Spaces of) multilinear mappings, polynomials
47A12Numerical range and numerical radius of linear operators
[1]Bonsall, F. F.; Cain, B. E.; Schneider, H.: The numerical range of a continuous mapping of a normed space, Aequationes math. 2, 86-93 (1968) · Zbl 0162.20101 · doi:10.1007/BF01833492
[2]Choi, Y. S.; García, D.; Kim, S. G.; Maestre, M.: The polynomial numerical index of a Banach space, Proc. Edinburgh math. Soc. 49, 39-52 (2006) · Zbl 1122.46002 · doi:10.1017/S0013091502000810
[3]Choi, Y. S.; García, D.; Kim, S. G.; Maestre, M.: Composition, numerical range and aron-berner extension, Math. scand. 103, 97-110 (2008) · Zbl 1157.46022
[4]Choi, Y. S.; García, D.; Maestre, M.; Martín, M.: Polynomial numerical index for some complex vector-valued function spaces, Quart. J. Math. 59, 455-474 (2008) · Zbl 1165.46021 · doi:10.1093/qmath/ham054
[5]Deville, R.; Godefroy, G.; Zizler, V.: Smoothness and renormings in Banach spaces, Pitman monographs and surveys in pure and appl. Math. 64 (1993) · Zbl 0782.46019
[6]Dineen, S.: Complex analysis on infinite dimensional spaces, Springer monographs in mathematics (1999)
[7]Duncan, J.; Mcgregor, C.; Pryce, J.; White, A.: The numerical index of a normed space, J. London math. Soc. 2, 481-488 (1970) · Zbl 0197.10402
[8]Ed-Dari, E.; Khamsi, M. A.: The numerical index of the lp space, Proc. amer. Math. soc. 134, 2019-2025 (2006) · Zbl 1097.46010 · doi:10.1090/S0002-9939-05-08231-6
[9]Harris, L. A.: The numerical range of holomorphic functions in Banach spaces, Amer. J. Math. 93, 1005-1019 (1971) · Zbl 0237.58010 · doi:10.2307/2373743
[10]Martín, V. Kadets.M.; Payá, R.: Recent progress and open questions on the numerical index of Banach spaces, Rev. R. Acad. cienc. Serie A. Mat. 100, 155-182 (2006) · Zbl 1111.46007
[11]S.G. Kim, The polynomial numerical index of the Lp space, preprint, 2006.
[12]Kim, S. G.; Martín, M.; Merí, J.: On the polynomial numerical index of the real spaces c0,1 and , J. math. Anal. appl. 337, 98-106 (2008) · Zbl 1125.46033 · doi:10.1016/j.jmaa.2007.03.101
[13]Lee, H. J.: Banach spaces with polynomial numerical index 1, Bull. London math. Soc. 40, 193-198 (2008) · Zbl 1153.46028 · doi:10.1112/blms/bdm113
[14]Martín, M.; Merí, J.; Rodríguez-Palacios, A.: Finite-dimensional Banach spaces with numerical index zero, Indiana univ. Math. J. 53, 1279-1289 (2004) · Zbl 1090.46005 · doi:10.1512/iumj.2004.53.2447
[15]H. Rosenthal, The Lie algebra of a Banach Space in: Banach Spaces (Columbia, Mo., 1984), Lecture Notes in Math., vol. 1166, Springer-Verlag, Berlin, 1985, pp. 129 – 157. · Zbl 0613.46016
[16]Singer, I.: Bases in Banach spaces I, Die grundlehren der mathematischen wissenschaften, band 154 (1970)
[17]Tuy, H.: Convex analysis and global optimization, (1998)