Browse > Article
http://dx.doi.org/10.4134/BKMS.b150851

THE UNIT BALL OF 𝓛(2ℝ2h(w))  

Kim, Sung Guen (Department of Mathematics Kyungpook National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.2, 2017 , pp. 417-428 More about this Journal
Abstract
We classify the extreme bilinear forms of the unit ball of the space of bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms.
Keywords
bilinear forms; extreme points; hexagonal norms on ${\mathbb{R}}^2$;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
연도 인용수 순위
1 S. G. Kim, Exposed bilinear forms of $L(^2d_{*}(1,w)^2)$, Kyungpook Math. J. 55 (2015), no. 1, 119-126.   DOI
2 S. G. Kim, Exposed 2-homogeneous polynomials on the 2-dimensional real predual of Lorentz sequence space, Mediterr. J. Math. 13 (2016), no. 5, 2827-2839.   DOI
3 S. G. Kim, Extremal problems for $L_s(^2{\mathbb{R}}^2_{h(w)})$, to appear in the Kyungpook Math. J. 57.
4 S. G. Kim, The geometry of the space of symmetric bilinear forms on $\mathbb{R}^2$ with octagonalnorm, Kyungpook Math. J. 56 (2016), 781-791.   DOI
5 S. G. Kim and S. H. Lee, Exposed 2-homogeneous polynomials on Hilbert spaces, Proc. Amer. Math. Soc. 131 (2003), no. 2, 449-453.   DOI
6 J. Lee and K. S. Rim, Properties of symmetric matrices, J. Math. Anal. Appl. 305(2005), no. 1, 219-226.   DOI
7 G. A. Munoz-Fernandez, S. Revesz, and J. B. Seoane-Sepulveda, Geometry of homoge-neous polynomials on non symmetric convex bodies, Math. Scand. 105 (2009), no. 1, 147-160.   DOI
8 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.   DOI
9 R. A. Ryan and B. Turett, Geometry of spaces of polynomials, J. Math. Anal. Appl. 221 (1998), no. 2, 698-711.   DOI
10 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), no. 1, 25-39.
11 Y. S. Choi, H. Ki, and S. G. Kim, Extreme polynomials and multilinear forms on $l_1$, J. Math. Anal. Appl. 228 (1998), no. 2, 467-482.   DOI
12 Y. S. Choi and S. G. Kim, The unit ball of $P(^2l^2_2)$, Arch. Math. (Basel) 71 (1998), no. 6, 472-480.   DOI
13 Y. S. Choi and S. G. Kim, Extreme polynomials on $c_0$, Indian J. Pure Appl. Math. 29 (1998), no. 10, 983-989.
14 Y. S. Choi and S. G. Kim, Smooth points of the unit ball of the space $P(^2l_1)$, Results Math. 36 (1999), no. 1-2, 26-33.   DOI
15 Y. S. Choi and S. G. Kim, Exposed points of the unit balls of the spaces $P(^2l^2_p)$ (p = 1, 2, ${\infty}$), Indian J. Pure Appl. Math. 35 (2004), no. 1, 37-41.
16 B. C. Grecu, G. A. Munoz-Fernandez, and J. B. Seoane-Sepulveda, Unconditional con-stants and polynomial inequalities, J. Approx. Theory 161 (2009), no. 2, 706-722.   DOI
17 S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer-Verlag, London, 1999.
18 S. Dineen, Extreme integral polynomials on a complex Banach space, Math. Scand. 92 (2003), no. 1, 129-140.   DOI
19 B. C. Grecu, Geometry of 2-homogeneous polynomials on $l_p$ spaces, 1 < p < ${\infty}$, J. Math. Anal. Appl. 273 (2002), no. 2, 262-282.   DOI
20 S. G. Kim, Exposed 2-homogeneous polynomials on $P(^2l^2_p) (1{\leq}p{\leq}{\infty})$, Math. Proc. R. Ir. Acad. 107 (2007), no. 2, 123-129.   DOI
21 S. G. Kim, Smooth polynomials of $P(^2d_{*}(1,w)^2)$, Math. Proc. R. Ir. Acad. 113A (2013), no. 1, 45-58.
22 S. G. Kim, The unit ball of $L_s(^2l^2_{\infty})$, Extracta Math. 24 (2009), no. 1, 17-29.
23 S. G. Kim, The unit ball of $P(^2d_{*}(1,w)^2)$, Math. Proc. R. Ir. Acad. 111A (2011), no. 2, 79-94.
24 S. G. Kim, The unit ball of $L_s(^2d_{*}(1,w)^2)$, Kyungpook Math. J. 53 (2013), no. 2, 295-306.   DOI
25 S. G. Kim, Extreme bilinear forms of $L(^2d_{*}(1,w)^2)$, Kyungpook Math. J. 53 (2013), no. 4, 625-638.   DOI
26 S. G. Kim, Exposed symmetric bilinear forms of $L_s(^2d_{*}(1,w)^2)$, Kyungpook Math. J. 54 (2014), no. 3, 341-347.   DOI