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Exposed Bilinear Forms of 𝓛(2d*(1, w)2)
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  • Journal title : Kyungpook mathematical journal
  • Volume 55, Issue 1,  2015, pp.119-126
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2015.55.1.119
 Title & Authors
Exposed Bilinear Forms of 𝓛(2d*(1, w)2)
Kim, Sung Guen;
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 Abstract
First we present the explicit formula for the norm of a (continuous) linear functional of . Using this formula and results of [16] and [17], we show that every extreme bilinear form of the unit ball of is exposed.
 Keywords
Extreme and exposed bilinear forms;the 2-dimensional real predual of the Lorentz sequence space;
 Language
English
 Cited by
 References
1.
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.

2.
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. crossref(new window)

3.
Y. S. Choi and S. G. Kim, The unit ball of $P(^2l^2_2)$, Arch. Math. (Basel), 71(1998), 472-480. crossref(new window)

4.
Y. S. Choi and S. G. Kim, Extreme polynomials on $c_0$, Indian J. Pure Appl. Math., 29(1998), 983-989.

5.
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. crossref(new window)

6.
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.

7.
S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer-Verlag, London (1999).

8.
S. Dineen, Extreme integral polynomials on a complex Banach space, Math. Scand., 92(2003), 129-140.

9.
B. C. Grecu, Geometry of 2-homogeneous polynomials on lp spaces, 1 < p ,< ${\infty}$;, J. Math. Anal. Appl., 273(2002), 262-282 . crossref(new window)

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. crossref(new window)

11.
S. G. Kim, Exposed 2-homogeneous polynomials on $P(^2l^2_p)$ $1{\leq}p{\leq}{\infty}$, Math. Proc. Royal Irish Acad., 107(2007), 123-129. crossref(new window)

12.
S. G. Kim, The unit ball of $L_s(^2l^2_{\infty})$, Extracta Math., 24(2009), 17-29.

13.
S. G. Kim, The unit ball of $P^2d_*(1,w)^2$, Math. Proc. Royal Irish Acad., 111(2)(2011), 79-94.

14.
S. G. Kim, The unit ball of $L_s(^2d_*(1;w)^2)$, Kyungpook Math. J., 53(2013), 295-306. crossref(new window)

15.
S. G. Kim, Smooth polynomials of $P(^2d_*(1,w)^2)$, Math. Proc. Royal Irish Acad., 113A(1)(2013), 45-58.

16.
S. G. Kim, Extreme bilinear forms of $L(^2d_*(1,w)^2)$, Kyungpook Math. J., 53(2013), 625-638. crossref(new window)

17.
S. G. Kim, Exposed symmetric bilinear forms of $L(^2d_*(1,w)^2)$, Kyungpook Math. J., 54(2014), 341-347. crossref(new window)

18.
S. G. Kim and S. H. Lee, Exposed 2-homogeneous polynomials on Hilbert spaces, Proc. Amer. Math. Soc., 131(2003), 449-453. crossref(new window)

19.
J. Lee and K. S. Rim, Properties of symmetric matrices, J. Math. Anal. Appl., 305(2005), 219-226. crossref(new window)

20.
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.

21.
G. A. Munoz-Fernandez and J.B. Seoane-Sepulveda, Geometry of Banach spaces of trinomials, J. Math. Anal. Appl., 340(2008), 1069-1087. crossref(new window)

22.
R. A. Ryan and B. Turett, Geometry of spaces of polynomials, J. Math. Anal. Appl., 221(1998), 698-711. crossref(new window)