Browse > Article
http://dx.doi.org/10.4134/CKMS.c190300

EXTREME POINTS OF THE SPACE 𝓛(2𝒍∞)  

Kim, Sung Guen (Department of Mathematics Kyungpook National University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.3, 2020 , pp. 799-807 More about this Journal
Abstract
We investigate extreme points of the unit ball of the space 𝓛(2𝒍∞).
Keywords
extreme points;
Citations & Related Records
Times Cited By KSCI : 10  (Citation Analysis)
연도 인용수 순위
1 S. G. Kim, The unit ball of ${\mathcal{L}}(^2{\mathbb{R}}^2_{h(w)})$, Bull. Korean Math. Soc. 54 (2017), no. 2, 417-428. https://doi.org/10.4134/BKMS.b150851   DOI
2 S. G. Kim, Extremal problems for ${\mathcal{L}}_s(^2{\mathbb{R}}^2_{h(w)})$, Kyungpook Math. J. 57 (2017), no. 2, 223- 232.   DOI
3 S. G. Kim, The unit ball of ${\mathcal{L}}_s(^2l^3_{\infty})$, Comment. Math. 57 (2017), no. 1, 1-7. https://doi.org/10.14708/cm.v57i1.1230
4 S. G. Kim, The geometry of ${\mathcal{L}}_s(^3l^2_{\infty})$, Commun. Korean Math. Soc. 32 (2017), no. 4, 991-997.   DOI
5 S. G. Kim, Extreme 2-homogeneous polynomials on the plane with a hexagonal norm and applications to the polarization and unconditional constants, Studia Sci. Math. Hungar. 54 (2017), no. 3, 362-393. https://doi.org/10.1556/012.2017.54.3.1371   DOI
6 S. G. Kim, The geometry of ${\mathcal{L}}(^3l^2_{\infty})$ and optimal constants in the Bohnenblust-Hille inequality for multilinear forms and polynomials, Extracta Math. 33 (2018), no. 1, 51-66.   DOI
7 S. G. Kim, Extreme bilinear forms on ${\mathbb{R}}^n$ with the supremum norm, Period. Math. Hungar. 77 (2018), no. 2, 274-290. https://doi.org/10.1007/s10998-018-0246-z   DOI
8 S. G. Kim, Exposed polynomials of {\mathcal{P}}(^2{\mathbb{R}}^2_{h(\frac{1}{2})}), Extracta Math. 33 (2018), no. 2, 127-143.   DOI
9 S. G. Kim, The unit ball of the space of bilinear forms on ${\mathbb{R}}^3$ with the supremum norm, Commun. Korean Math. Soc. 34 (2019), no. 2, 487-494.   DOI
10 S. G. Kim and S. H. Lee, Exposed 2-homogeneous polynomials on Hilbert spaces, Proc. Amer. Math. Soc. 131 (2003), no. 2, 449-453. https://doi.org/10.1090/S0002-9939-02-06544-9   DOI
11 G. A. Munoz-Fernandez and J. B. Seoane-Sepulveda, Geometry of Banach spaces of trinomials, J. Math. Anal. Appl. 340 (2008), no. 2, 1069-1087. https://doi.org/10.1016/j.jmaa.2007.09.010   DOI
12 A. G. Konheim and T. J. Rivlin, Extreme points of the unit ball in a space of real polynomials, Amer. Math. Monthly 73 (1966), 505-507. https://doi.org/10.2307/2315472   DOI
13 L. Milev and N. Naidenov, Strictly definite extreme points of the unit ball in a polynomial space, C. R. Acad. Bulgare Sci. 61 (2008), no. 11, 1393-1400.
14 L. Milev and N. Naidenov, Semidefinite extreme points of the unit ball in a polynomial space, J. Math. Anal. Appl. 405 (2013), no. 2, 631-641. https://doi.org/10.1016/j.jmaa.2013.04.026   DOI
15 G. A. Munoz-Fernandez, D. Pellegrino, J. B. Seoane-Sepulveda, and A. Weber, Supremum norms for 2-homogeneous polynomials on circle sectors, J. Convex Anal. 21 (2014), no. 3, 745-764.
16 G. A. Munoz-Fernandez, S. Gy. Revesz, and J. B. Seoane-Sepulveda, Geometry of homogeneous polynomials on non symmetric convex bodies, Math. Scand. 105 (2009), no. 1, 147-160. https://doi.org/10.7146/math.scand.a-15111   DOI
17 S. Neuwirth, The maximum modulus of a trigonometric trinomial, J. Anal. Math. 104 (2008), 371-396. https://doi.org/10.1007/s11854-008-0028-2   DOI
18 R. A. Ryan and B. Turett, Geometry of spaces of polynomials, J. Math. Anal. Appl. 221 (1998), no. 2, 698-711. https://doi.org/10.1006/jmaa.1998.5942   DOI
19 W. Cavalcante and D. Pellegrino, Geometry of the closed unit ball of the space of bilinear forms on $l^2_{\infty}$, arXiv:1603.01535v2.
20 R. M. Aron and M. Klimek, Supremum norms for quadratic polynomials, Arch. Math. (Basel) 76 (2001), no. 1, 73-80. https://doi.org/10.1007/s000130050544   DOI
21 Y. S. Choi and S. G. Kim, The unit ball of ${\mathcal{P}}(^2l_2^2)$, Arch. Math. (Basel) 71 (1998), no. 6, 472-480. https://doi.org/10.1007/s000130050292   DOI
22 Y. S. Choi and S. G. Kim, Extreme polynomials on $c_0$, Indian J. Pure Appl. Math. 29 (1998), no. 10, 983-989.
23 Y. S. Choi and S. G. Kim, Smooth points of the unit ball of the space ${\mathcal{P}}(^2l_1)$, Results Math. 36 (1999), no. 1-2, 26-33. https://doi.org/10.1007/BF03322099   DOI
24 J. L. Gamez-Merino, G. A. Munoz-Fernandez, V. M. Sanchez, and J. B. Seoane-Sepulveda, Inequalities for polynomials on the unit square via the Krein-Milman theorem, J. Convex Anal. 20 (2013), no. 1, 125-142.
25 Y. S. Choi and S. G. Kim, Exposed points of the unit balls of the spaces ${\mathcal{P}}(^2l^2_p)$ ($p=1,2,{\infty}$), Indian J. Pure Appl. Math. 35 (2004), no. 1, 37-41.
26 Y. S. Choi, S. G. Kim, and H. Ki, Extreme polynomials and multilinear forms on $l_1$, J. Math. Anal. Appl. 228 (1998), no. 2, 467-482. https://doi.org/10.1006/jmaa.1998.6161   DOI
27 S. Dineen, Complex analysis on infinite-dimensional spaces, Springer Monographs in Mathematics, Springer-Verlag London, Ltd., London, 1999. https://doi.org/10.1007/978-1-4471-0869-6
28 B. C. Grecu, Geometry of three-homogeneous polynomials on real Hilbert spaces, J. Math. Anal. Appl. 246 (2000), no. 1, 217-229. https://doi.org/10.1006/jmaa.2000.6783   DOI
29 B. C. Grecu, Smooth 2-homogeneous polynomials on Hilbert spaces, Arch. Math. (Basel) 76 (2001), no. 6, 445-454. https://doi.org/10.1007/PL00000456   DOI
30 B. C. Grecu, Geometry of 2-homogeneous polynomials on $l_p$ spaces, $1   DOI
31 S. G. Kim, The unit ball of ${\mathcal{P}}(^2D_*(1,\;W)^2)$, Math. Proc. R. Ir. Acad. 111A (2011), no. 2, 79-94.
32 B. C. Grecu, Extreme 2-homogeneous polynomials on Hilbert spaces, Quaest. Math. 25 (2002), no. 4, 421-435. https://doi.org/10.2989/16073600209486027   DOI
33 B. C. Grecu, Geometry of homogeneous polynomials on two-dimensional real Hilbert spaces, J. Math. Anal. Appl. 293 (2004), no. 2, 578-588. https://doi.org/10.1016/j.jmaa.2004.01.020   DOI
34 B. C. Grecu, G. A. Munoz-Fernandez, and J. B. Seoane-Sepulveda, The unit ball of the complex ${\mathcal{P}}(^3H)$, Math. Z. 263 (2009), no. 4, 775-785. https://doi.org/10.1007/s00209-008-0438-y   DOI
35 S. G. Kim, Exposed 2-homogeneous polynomials on ${\mathcal{P}}(^2l^2_P)$ for $1{\leq}p{\leq}{\infty}$, Math. Proc. R. Ir. Acad. 107 (2007), no. 2, 123-129. https://doi.org/10.3318/PRIA.2007.107.2.123   DOI
36 S. G. Kim, The unit ball of ${\mathcal{L_s(^2l^2_{\infty})}$, Extracta Math. 24 (2009), no. 1, 17-29.
37 S. G. Kim, The unit ball of ${\mathcal{L}}_s(^2d_*(1,\;w)^2)$, Kyungpook Math. J. 53 (2013), no. 2, 295-306. https://doi.org/10.5666/KMJ.2013.53.2.295   DOI
38 S. G. Kim, Smooth polynomials of ${\mathcal{P}}(^2D_*(1,\;W)^2)$, Math. Proc. R. Ir. Acad. 113A (2013), no. 1, 45-58. https://doi.org/10.3318/PRIA.2013.113.05   DOI
39 S. G. Kim, Exposed symmetric bilinear forms of ${\mathcal{L}}_s(^2d_*(1,\;w)^2)$, Kyungpook Math. J. 54 (2014), no. 3, 341-347. https://doi.org/10.5666/KMJ.2014.54.3.341   DOI
40 S. G. Kim, Extreme bilinear forms of ${\mathcal{L}}(^2d_*(1,\;w)^2)$, Kyungpook Math. J. 53 (2013), no. 4, 625-638. https://doi.org/10.5666/KMJ.2013.53.4.625   DOI
41 S. G. Kim, Polarization and unconditional constants of ${\mathcal{P}}(^2d_*(1,\;w)^2)$, Commun. Korean Math. Soc. 29 (2014), no. 3, 421-428. https://doi.org/10.4134/CKMS.2014.29.3.421   DOI
42 S. G. Kim, Exposed bilinear forms of ${\mathcal{L}}(^2d_*(1,\;w)^2)$, Kyungpook Math. J. 55 (2015), no. 1, 119-126. https://doi.org/10.5666/KMJ.2015.55.1.119   DOI
43 S. G. Kim, Exposed 2-homogeneous polynomials on the two-dimensional real predual of Lorentz sequence space, Mediterr. J. Math. 13 (2016), no. 5, 2827-2839. https://doi.org/10.1007/s00009-015-0658-4   DOI