Polynomial numerical indices of 𝐶(𝐾) and 𝐿₁(𝜇)

García, Domingo; Grecu, Bogdan; Maestre, Manuel; Martín, Miguel; Merí, Javier

doi:10.1090/S0002-9939-2013-11850-2

Polynomial numerical indices of $\boldsymbol {C(K)}$ and $\boldsymbol {L_1(\mu )}$
HTML articles powered by AMS MathViewer

by Domingo García, Bogdan C. Grecu, Manuel Maestre, Miguel Martín and Javier Merí PDF

Proc. Amer. Math. Soc. 142 (2014), 1229-1235 Request permission

Abstract:

We estimate the polynomial numerical indices of the spaces $C(K)$ and $L_1(\mu )$.

References

Kostyantyn Boyko, Vladimir Kadets, Miguel Martín, and Dirk Werner, Numerical index of Banach spaces and duality, Math. Proc. Cambridge Philos. Soc. 142 (2007), no. 1, 93–102. MR 2296393, DOI 10.1017/S0305004106009650
Yun Sung Choi, Domingo Garcia, Sung Guen Kim, and Manuel Maestre, The polynomial numerical index of a Banach space, Proc. Edinb. Math. Soc. (2) 49 (2006), no. 1, 39–52. MR 2202141, DOI 10.1017/S0013091502000810
Yun Sung Choi, Domingo García, Manuel Maestre, and Miguel Martín, Polynomial numerical index for some complex vector-valued function spaces, Q. J. Math. 59 (2008), no. 4, 455–474. MR 2461268, DOI 10.1093/qmath/ham054
Yun Sung Choi and Sung Guen Kim, Norm or numerical radius attaining multilinear mappings and polynomials, J. London Math. Soc. (2) 54 (1996), no. 1, 135–147. MR 1395073, DOI 10.1112/jlms/54.1.135
Domingo García, Bogdan C. Grecu, Manuel Maestre, Miguel Martín, and Javier Merí, Two-dimensional Banach spaces with polynomial numerical index zero, Linear Algebra Appl. 430 (2009), no. 8-9, 2488–2500. MR 2508308, DOI 10.1016/j.laa.2008.12.020
Vladimir Kadets, Miguel Martín, Javier Merí, and Varvara Shepelska, Lushness, numerical index one and duality, J. Math. Anal. Appl. 357 (2009), no. 1, 15–24. MR 2526802, DOI 10.1016/j.jmaa.2009.03.055
Vladimir Kadets, Miguel Martín, and Rafael Payá, Recent progress and open questions on the numerical index of Banach spaces, RACSAM. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 100 (2006), no. 1-2, 155–182 (English, with English and Spanish summaries). MR 2267407
Jaegil Kim and Han Ju Lee, Strong peak points and strongly norm attaining points with applications to denseness and polynomial numerical indices, J. Funct. Anal. 257 (2009), no. 4, 931–947. MR 2535458, DOI 10.1016/j.jfa.2008.11.024
Sung Guen Kim, Miguel Martín, and Javier Merí, On the polynomial numerical index of the real spaces $c_0,\ l_1$ and $l_\infty$, J. Math. Anal. Appl. 337 (2008), no. 1, 98–106. MR 2356057, DOI 10.1016/j.jmaa.2007.03.101
H. Elton Lacey, The isometric theory of classical Banach spaces, Die Grundlehren der mathematischen Wissenschaften, Band 208, Springer-Verlag, New York-Heidelberg, 1974. MR 0493279
Han Ju Lee, Banach spaces with polynomial numerical index 1, Bull. Lond. Math. Soc. 40 (2008), no. 2, 193–198. MR 2414778, DOI 10.1112/blms/bdm113
Han Ju Lee and Miguel Martín, Polynomial numerical indices of Banach spaces with 1-unconditional bases, Linear Algebra Appl. 437 (2012), no. 8, 2001–2008. MR 2950467, DOI 10.1016/j.laa.2011.05.043
Han Ju Lee, Miguel Martín, and Javier Merí, Polynomial numerical indices of Banach spaces with absolute norm, Linear Algebra Appl. 435 (2011), no. 2, 400–408. MR 2782789, DOI 10.1016/j.laa.2011.01.037
Ángel Rodríguez Palacios, Numerical ranges of uniformly continuous functions on the unit sphere of a Banach space, J. Math. Anal. Appl. 297 (2004), no. 2, 472–476. Special issue dedicated to John Horváth. MR 2088672, DOI 10.1016/j.jmaa.2004.03.012