Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (κ²½λΆλŒ€ν•™κ΅ μžμ—°κ³Όν•™λŒ€ν•™ μˆ˜ν•™κ³Ό)
ꢌ호 ν‘œμ§€
DOI QRμ½”λ“œ

DOI QR Code

Exposed Symmetric Bilinear Forms of 𝓛s(2d*(1, Ο‰)2)

  • Kim, Sung Guen (Department of Mathematics, Kyungpook National University)
  • Received : 2013.05.02
  • Accepted : 2013.10.15
  • Published : 2014.09.23
Download PDF
⟨ Previous Next ⟩

Abstract

We classify the exposed symmetric bilinear forms of the unit ball of $\mathcal{L}_s(^2d_*(1,{\omega})^2)$.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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(1)(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(2)(1998), 467-482. https://doi.org/10.1006/jmaa.1998.6161
  3. Y. S. Choi and S. G. Kim, The unit ball of P($^{2}l^{2}_{2}$), Arch. Math. (Basel), 71(6)(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(10)(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(1-2)(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 P($^{2}l^{2}_{p}$) (p =1, 2,${\infty}$), Indian J. Pure Appl. Math., 35(1)(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(1)(2003), 129-140. https://doi.org/10.7146/math.scand.a-14397
  9. B. C. Grecu, Geometry of 2-homogeneous polynomials on $l_p$ spaces, 1 < p < ${\infty}$, J. Math. Anal. Appl., 273(2)(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 con-stants and polynomial inequalities, J. Approx. Theory, 161(2)(2009), 706-722. https://doi.org/10.1016/j.jat.2008.12.001
  11. S. G. Kim, Exposed 2-homogeneous polynomials on P($^{2}l^{2}_{p}$) (1 ${\leq}$ p ${\leq}$ ${\infty}$), Math. Proc. Royal Irish Acad., 107(2)(2007), 123-129. https://doi.org/10.3318/PRIA.2007.107.2.123
  12. S. G. Kim, The unit ball of $L_s$($^{2}l^{2}_{\infty}$), Extracta Math., 24(1)(2009), 17-29.
  13. S. G. Kim, The unit ball of P($^2d_{\ast}(1,w)^2$), Math. Proc. Royal Irish Acad., 111(2011), 77-92. https://doi.org/10.3318/PRIA.2011.111.1.9
  14. S. G. Kim, The unit ball of $L_s$($^2d_{\ast}(1,w)^2$), Kyungpook Math. J., 53(2)(2013), 295-306. https://doi.org/10.5666/KMJ.2013.53.2.295
  15. S. G. Kim, Smooth polynomials of P($^2d_{\ast}(1,w)^2$), Math. Proc. Royal Irish Acad., 113(1)(2013), 45-58. https://doi.org/10.3318/PRIA.2013.113.05
  16. S. G. Kim, Extreme bilinear forms of L($^2d_{\ast}(1,w)^2$), Kyungpook Math. J., 53(4)(2013), 625-638. https://doi.org/10.5666/KMJ.2013.53.4.625
  17. S. G. Kim and S. H. Lee, Exposed 2-homogeneous polynomials on Hilbert spaces, Proc. Amer. Math. Soc., 131(2)(2003), 449-453. https://doi.org/10.1090/S0002-9939-02-06544-9
  18. J. Lee and K. S. Rim, Properties of symmetric matrices, J. Math. Anal. Appl., 305(1)(2005), 219-226. https://doi.org/10.1016/j.jmaa.2004.11.011
  19. G. A. Munoz-Fernandez, S. Revesz and J. B. Seoane-Sepulveda, Geometry of homo-geneous polynomials on non symmetric convex bodies, Math. Scand., 105(1)(2009), 147-160. https://doi.org/10.7146/math.scand.a-15111
  20. G. A. Munoz-Fernandez and J. B. Seoane-Sepulveda, Geometry of Banach spaces of trinomials, J. Math. Anal. Appl., 340(2)(2008), 1069-1087. https://doi.org/10.1016/j.jmaa.2007.09.010
  21. R. A. Ryan and B. Turett, Geometry of spaces of polynomials, J. Math. Anal. Appl., 221(2)(1998), 698-711. https://doi.org/10.1006/jmaa.1998.5942

Cited by

  1. Exposed Bilinear Forms of 𝓛(2d*(1, w)2) vol.55, pp.1, 2015, https://doi.org/10.5666/KMJ.2015.55.1.119
  2. Exposed 2-Homogeneous Polynomials on the two-Dimensional Real Predual of Lorentz Sequence Space vol.13, pp.5, 2016, https://doi.org/10.1007/s00009-015-0658-4
  3. The Geometry of the Space of Symmetric Bilinear Forms on ℝ2with Octagonal Norm vol.56, pp.3, 2016, https://doi.org/10.5666/KMJ.2016.56.3.781
  4. Extreme bilinear forms on $$\mathbb {R}^n$$Rn with the supremum norm vol.77, pp.2, 2018, https://doi.org/10.1007/s10998-018-0246-z