Browse > Article
http://dx.doi.org/10.5666/KMJ.2017.57.2.223

Extremal Problems for 𝓛s(22h(w))  

Kim, Sung Guen (Department of Mathematics, Kyungpook National University)
Publication Information
Kyungpook Mathematical Journal / v.57, no.2, 2017 , pp. 223-232 More about this Journal
Abstract
We classify the extreme and exposed symmetric bilinear forms of the unit ball of the space of symmetric bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms. We also show that every extreme symmetric bilinear forms of the unit ball of the space of symmetric bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms is exposed.
Keywords
symmetric bilinear forms; extreme points; exposed points; hexagonal norms on ${\mathbb{R}}^2$;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
연도 인용수 순위
1 S. G. Kim, The unit ball of ${\mathcal{L}}_s(^2l^2_{\infty})$, Extracta Math., 24(2009), 17-29.
2 S. G. Kim, The unit ball of ${\mathcal{P}}(^2d_*(1,w)^2)$, Math. Proc. Royal Irish Acad., 111A(2011), 79-94.
3 S. G. Kim, The unit ball of ${\mathcal{L}}_s(^2d_*(1,w)^2)$, Kyungpook Math. J., 53(2013), 295-306.   DOI
4 S. G. Kim, Smooth polynomials of ${\mathcal{P}}(^2d_*(1,w)^2)$, Math. Proc. Royal Irish Acad., 113A(2013), 45-58.
5 S. G. Kim, Extreme bilinear forms of ${\mathcal{L}}(^2d_*(1,w)^2)$, Kyungpook Math. J., 53(2013), 625-638.   DOI
6 S. G. Kim, Exposed symmetric bilinear forms of ${\mathcal{L}}_s(^2d_*(1,w)^2)$, Kyungpook Math. J., 54(2014), 341-347.   DOI
7 S. G. Kim, Exposed bilinear forms of ${\mathcal{L}}(^2d_*(1,w)^2)$, Kyungpook Math. J., 55(2015), 119-126.   DOI
8 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
9 S. G. Kim, The unit ball of ${\mathcal{L}}(^2{\mathbb{R}}^2_h_{(w)})$, Bull. Korean Math. Soc., 54(2017), 417-428.
10 S. G. Kim and S. H. Lee, Exposed 2-homogeneous polynomials on Hilbert spaces, Proc. Amer. Math. Soc., 131(2003), 449-453.   DOI
11 J. Lee and K. S. Rim, Properties of symmetric matrices, J. Math. Anal. Appl., 305(2005), 219-226.   DOI
12 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
13 G. A. Munoz-Fernandez and J. B. Seoane-Sepulveda, Geometry of Banach spaces of trinomials, J. Math. Anal. Appl., 340(2008), 1069-1087.   DOI
14 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), 37-41.
15 R. A. Ryan and B. Turett, Geometry of spaces of polynomials, J. Math. Anal. Appl., 221(1998), 698-711.   DOI
16 R. M. Aron, Y. S. Choi, S. G. Kim and M. Maestre, Local properties of polynomials on a Banach space, Illinois J. Math., 45(2001), 25-39.
17 Y. S. Choi, H. Ki and S. G. Kim, Extreme polynomials and multilinear forms on $l_1$, J. Math. Anal. Appl., 228(1998), 467-482.   DOI
18 Y. S. Choi and S. G. Kim, The unit ball of ${\mathcal{P}}(^2l^2_2)$, Arch. Math.(Basel), 71(1998), 472-480.   DOI
19 Y. S. Choi and S. G. Kim, Extreme polynomials on $c_0$, Indian J. Pure Appl. Math., 29(1998), 983-989.
20 Y. S. Choi and S. G. Kim, Smooth points of the unit ball of the space ${\mathcal{P}}(^2l_1)$, Results Math., 36(1999), 26-33.   DOI
21 S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer-Verlag, London (1999).
22 S. Dineen, Extreme integral polynomials on a complex Banach space, Math. Scand., 92(2003), 129-140.   DOI
23 B. C. Grecu, Geometry of 2-homogeneous polynomials on lp spaces, $1   DOI
24 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
25 S. G. Kim, Exposed 2-homogeneous polynomials on ${\mathcal{P}}(^2l^2_p)\;(1{\leq}p{\leq}{\infty}),$, Math. Proc. Royal Irish Acad., 107A(2007), 123-129.