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http://dx.doi.org/10.5666/KMJ.2013.53.4.625

Extreme Bilinear Forms of $\mathcal{L}(^2d_*(1,w)^2)$  

Kim, Sung Guen (Department of Mathematics, Kyungpook National University)
Publication Information
Kyungpook Mathematical Journal / v.53, no.4, 2013 , pp. 625-638 More about this Journal
Abstract
First we present the explicit formula for the norm of a bilinear form on the 2-dimensional real predual of the Lorentz sequence space $d_*(1,w)^2$. Using this formula, we classify the extreme points of the unit ball of $\mathcal{L}(^2d_*(1,w)^2)$.
Keywords
extreme bilinear forms; the 2-dimensional real predual of the Lorentz sequence space;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 J. Lee and K. S. Rim, Properties of symmetric matrices, J. Math. Anal. Appl. 305(2005), 219-226.   DOI   ScienceOn
2 Y. S. Choi and S. G. Kim, Smooth points of the unit ball of the space $P(^2l_1)$, Results Math. 36(1999), 26-33.   DOI
3 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), 37-41.
4 S. Dineen, Complex Analysis on In nite Dimensional Spaces, Springer-Verlag, London (1999).
5 S. Dineen, Extreme integral polynomials on a complex Banach space Math. Scand. 92(2003), 129-140.   DOI
6 B. C. Grecu, G. A. Munoz-Fernandez and J.B. Seoane-Sepulveda, Unconditional con-stants and polynomial inequalities, J. Approx. Theory 161(2009), 706-722.   DOI   ScienceOn
7 S. G. Kim, Exposed 2-homogeneous polynomials on $P(^2l^2_p)(1{\leq}p{\leq}{\infty})$, Math. Proc. Royal Irish Acad. 107A(2007), 123-129.
8 S. G. Kim, The unit ball of $L_s(^2l^2_{\infty})$, Extracta Math. 24(2009), 17-29.
9 Y. S. Choi and S. G. Kim, The unit ball of $P(^2l^2_2)$, Arch. Math. (Basel) 71(1998), 472-480.   DOI
10 Y. S. Choi and S. G. Kim, Extreme polynomials on $c_0$, Indian J. Pure Appl. Math. 29(1998), 983-989.
11 S. G. Kim, The unit ball of $P(^2d_*(1,w)^2)$, Math. Proc. Royal Irish Acad. 111A(2011), 79-94.
12 S. G. Kim, Smooth polynomials of $P(^2d_*(1,w)^2)$, Math. Proc. Royal Irish Acad. 113A(2013), 45-58.
13 S. G. Kim and S. H. Lee, Exposed 2-homogeneous polynomials on Hilbert spaces, Proc. Amer. Math. Soc. 131(2003), 449-453.   DOI   ScienceOn
14 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   ScienceOn
15 G. A. Munoz-Fernandez, S. Revesz and J. B. Seoane-Sepulveda, Geometry of ho-mogeneous polynomials on non symmetric convex bodies, Math. Scand. 105(2009), 147-160.   DOI
16 G. A. Munoz-Fernandez and J. B. Seoane-Sepulveda, Geometry of Banach spaces of trinomials, J. Math. Anal. Appl. 340(2008), 1069-1087.   DOI   ScienceOn
17 R. A. Ryan and B. Turett, Geometry of spaces of polynomials, J. Math. Anal. Appl. 221(1998), 698-711.   DOI   ScienceOn
18 S. G. Kim, The unit ball of $L_s(^2d_*(1,w)^2)$, Kyungpook Math. J. 53(2013), 295-306.   과학기술학회마을   DOI   ScienceOn
19 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.
20 B. C. Grecu, Geometry of 2-homogeneous polynomials on $l_p$ spaces, 1 < p < ${\infty}$, J. Math. Anal. Appl. 273(2002), 262-282.   DOI   ScienceOn