DOI QR코드

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Extremal Problems for 𝓛s(22h(w))

  • Kim, Sung Guen (Department of Mathematics, Kyungpook National University)
  • 투고 : 2015.03.11
  • 심사 : 2015.12.04
  • 발행 : 2017.06.23

초록

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.

키워드

참고문헌

  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. https://doi.org/10.1006/jmaa.1998.6161
  3. Y. S. Choi and S. G. Kim, The unit ball of ${\mathcal{P}}(^2l^2_2)$, Arch. Math.(Basel), 71(1998), 472-480. https://doi.org/10.1007/s000130050292
  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 ${\mathcal{P}}(^2l_1)$, Results Math., 36(1999), 26-33. https://doi.org/10.1007/BF03322099
  6. 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.
  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. https://doi.org/10.7146/math.scand.a-14397
  9. B. C. Grecu, Geometry of 2-homogeneous polynomials on lp spaces, $1; J. Math. Anal. Appl., 273(2002), 262-282 . https://doi.org/10.1016/S0022-247X(02)00217-2
  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. https://doi.org/10.1016/j.jat.2008.12.001
  11. 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.
  12. S. G. Kim, The unit ball of ${\mathcal{L}}_s(^2l^2_{\infty})$, Extracta Math., 24(2009), 17-29.
  13. S. G. Kim, The unit ball of ${\mathcal{P}}(^2d_*(1,w)^2)$, Math. Proc. Royal Irish Acad., 111A(2011), 79-94.
  14. S. G. Kim, The unit ball of ${\mathcal{L}}_s(^2d_*(1,w)^2)$, Kyungpook Math. J., 53(2013), 295-306. https://doi.org/10.5666/KMJ.2013.53.2.295
  15. S. G. Kim, Smooth polynomials of ${\mathcal{P}}(^2d_*(1,w)^2)$, Math. Proc. Royal Irish Acad., 113A(2013), 45-58.
  16. S. G. Kim, Extreme bilinear forms of ${\mathcal{L}}(^2d_*(1,w)^2)$, Kyungpook Math. J., 53(2013), 625-638. https://doi.org/10.5666/KMJ.2013.53.4.625
  17. S. G. Kim, Exposed symmetric bilinear forms of ${\mathcal{L}}_s(^2d_*(1,w)^2)$, Kyungpook Math. J., 54(2014), 341-347. https://doi.org/10.5666/KMJ.2014.54.3.341
  18. S. G. Kim, Exposed bilinear forms of ${\mathcal{L}}(^2d_*(1,w)^2)$, Kyungpook Math. J., 55(2015), 119-126. https://doi.org/10.5666/KMJ.2015.55.1.119
  19. S. G. Kim, Exposed 2-homogeneous polynomials on the two-dimensional real predual of Lorentz sequence space, Mediterr. J. Math., 13(2016), 2827-2839. https://doi.org/10.1007/s00009-015-0658-4
  20. S. G. Kim, The unit ball of ${\mathcal{L}}(^2{\mathbb{R}}^2_h_{(w)})$, Bull. Korean Math. Soc., 54(2017), 417-428.
  21. S. G. Kim and S. H. Lee, Exposed 2-homogeneous polynomials on Hilbert spaces, Proc. Amer. Math. Soc., 131(2003), 449-453. https://doi.org/10.1090/S0002-9939-02-06544-9
  22. J. Lee and K. S. Rim, Properties of symmetric matrices, J. Math. Anal. Appl., 305(2005), 219-226. https://doi.org/10.1016/j.jmaa.2004.11.011
  23. 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. https://doi.org/10.7146/math.scand.a-15111
  24. G. A. Munoz-Fernandez and J. B. Seoane-Sepulveda, Geometry of Banach spaces of trinomials, J. Math. Anal. Appl., 340(2008), 1069-1087. https://doi.org/10.1016/j.jmaa.2007.09.010
  25. R. A. Ryan and B. Turett, Geometry of spaces of polynomials, J. Math. Anal. Appl., 221(1998), 698-711. https://doi.org/10.1006/jmaa.1998.5942