The unit ball of L_s(²l³_∞)

• Autorzy: Kim S. G.

Identyfikatory

DOI

10.14708/cm.v57il.1230

• Języki publikacji: EN

Abstrakty

EN

We classify the extreme and exposed symmetric bilinear forms of the unit ball of the space L_s(²l³_∞).

Słowa kluczowe

EN

symmetric bilinear forms; extreme points; exposed points

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2017
• Tom: Vol 57, No. 1
• Strony: 1--7
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Kim S. G.

• Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea

Bibliografia

• [1] R. M. Aron, Y. S. Choi, S. G. Kim, and M. Maestre, Local properties o/polynomials on a Banach space, Illinois J. Math. 45 (2001), 25-39.
• [2] Y. S. Choi, H. Ki, and S. G. Kim, Extreme polynomials and multilinear forms on l1, J. Math. Anal. Appl. 228 (1998), 467-482.
• [3] Y. S. Choi and S. G. Kim, The unit ball o/ P(2l|), Arch. Math. 71 (1998), 472-480,
• DOI 10.1007/s000130050292.
• [4] Y. S. Choi and S. G. Kim, Extreme polynomials on Co, Indian J. Pure Appl. Math. 29 (1998), 983-989.
• [5] Y. S. Choi and S. G. Kim, Smooth points o/the unit ball o/ the space P (211), Results Math. 36 (1999), 26-33, DOI 10.1007/BF03322099.
• [6] Y. S. Choi and S. G. Kim, Exposed points o/ the unit balls o/ the spaces P (212) (p = 1,2, ∞), Indian J. Pure Appl. Math. 35 (2004), 37-41.
• [7] S. Dineen, Complex Analysis on In/inite Dimensional Spaces, Springer-Verlag, London 1999, DOI 10.1007/978-1-4471-0869-6.
• [8] S. Dineen, Extreme integral polynomials on a complex Banach space, Math. Scand. 92 (2003), 129-140, DOI 10.7146/math.scand.a-14397.
• [9] B. C. Grecu, Geometry o/2-homogeneous polynomials on lp spaces, 1 < p < , J. Math. Anal. Appl. 273 (2002), 262-282, DOI 10.1016/S0022-247X(02)00217-2.
• [10] B. C. Grecu, G. A. Munoz-Fernandez, and J. B. Seoane-Sepulveda, Unconditional constants and polynomial inequalities, J. Approx. Theory 161 (2009), 706-722, DOI 10.1016/j.jat.2008.12.001.
• [11] S. G. Kim, Exposed 2-homogeneous polynomials on P (2 lp ) (1 ≤ p ≤∞), Math. Proc. R. Ir. Acad. 107A (2007), 123-129, DOI 10.3318/PRIA.2007.107.2.123.
• [12] G. Kim, The unit ball of Ls (212∞), Extracta Math. 24 (2009), 17-29.
• [13] S. G. Kim, The unit ball of P(2d*(1, w)2), Math. Proc. R. Ir. Acad. 111A (2011), 79-94.
• [14] S. G. Kim, The unit ball of Ls(2d*(1, w)2), KyungpookMath. J. 53 (2013), 295-306,
• DOI 10.5666/KMJ.2013.53.2.295.
• [15] S. G. Kim, Smooth polynomials of P(2d* (1, w)2), Math. Proc. R. Ir. Acad. 113A (2013), 45-58.
• [16] S. G. Kim, Extreme bilinear forms of L(2d*(1, w)2), Kyungpook Math. J. 53 (2013), 625-638, DOI 10.5666/KMJ.2013.53.4.625.
• [17] S. G. Kim, Exposed symmetric bilinear forms of Ls (2 d* (1, w)2), Kyungpook Math. J. 54 (2014), 341-347, DOI 10.5666/KMJ.2014.54.3.341.
• [18] S. G. Kim, Exposed bilinear forms of L(2d* (1, w)2), Kyungpook Math. J. 55 (2015), 119-126, DOI 10.5666/KMJ.2015.55.1.119.
• [19] S. G. Kim, Exposed 2-homogeneous polynomials on the two-dimensional real predual of Lorentz sequence space, Mediterr. J. Math. 13 (2016), 2827-2839, DOI 10.1007/s00009-015-0658-4.
• [20] S. G. Kim, Extremal problems for Ls (2Rh(w)), Kyungpook Math. J. 57 (2017), to appear.
• [21] S. G. Kim and S. H. Lee, Exposed 2-homogeneous polynomials on Hilbert spaces, Proc. Amer. Math. Soc. 131 (2003), 449-453, DOI 10.1090/S0002-9939-02-06544-9.
• [22] J. Lee and K. S. Rim, Properties of symmetric matrices, J. Math. Anal. Appl. 305 (2005), 219-226, DOI 10.1016/j.jmaa.2004.11.011.
• [23] G. A. Munoz-Fernandez, S. Revesz, and J. B. Seoane-Sepulveda, Geometry of homogeneous polynomials on non symmetric convex bodies, Math. Scand. 105 (2009), 147-160, DOI 10.7146/math.scand.a-15111.
• [24] G. A. Munoz-Fernandez and J. B. Seoane-Sepulveda, Geometry of Banach spaces of trinomials, J. Math. Anal. Appl. 340 (2008), 1069-1087, DOI 10.1016/j.jmaa.2007.09.010.
• [25] R. A. Ryan and B. Turett, Geometry of spaces of polynomials, J. Math. Anal. Appl. 221 (1998), 698-711, DOI 10.1006/jmaa.1998.5942.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).