Author:
Sung Guen Kim Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea

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Abstract

For n,m≥ 2 this paper is devoted to the description of the sets of extreme and exposed points of the closed unit balls of (lnm) and s(lnm), where (lnm) is the space of n-linear forms on m with the supremum norm, and s(lnm) is the subspace of (lnm) consisting of symmetric n-linear forms. First we classify the extreme points of the unit balls of (lnm) and s(lnm), respectively. We show that ext B(lnm) ⊂ ext B(lnm+1), which answers the question in []. We show that every extreme point of the unit balls of (lnm) and s(lnm) is exposed, correspondingly. We also show that
extBs(ln2)=ext B(ln2)s(ln2),
ext Bs(l2m+1)ext B(l2m+1)s(l2m+1),
expBS(ln2)=expB(ln2)s(ln2)

and expBs(l2m+1)expB(l2m+1)s(l2m+1),

which answers the questions in [].

  • [1]

    Aron, R. M. and Klimek, M., Supremum norms for quadratic polynomials, Arch. Math. (Basel), 76 (2001), 7380.

  • [2]

    Cavalcante, W. and Pellegrino, D., Geometry of the closed unit ball of the space of bilinear forms on l 2, arXiv:1603.01535v2.

  • [3]

    Choi, Y. S., Ki, H. and Kim, S. G., Extreme polynomials and multilinear forms on l1, J. Math. Anal. Appl., 228 (1998), 467482.

  • [4]

    Choi, Y. S. and Kim, S. G., The unit ball of p( 2 l 2 2 ), Arch. Math. (Basel), 71 (1998), 472480.

  • [5]

    Choi, Y. S. and Kim, S. G., Extreme polynomials on c0, Indian J. Pure Appl. Math., 29 (1998), 983989.

  • [6]

    Choi, Y. S. and Kim, S. G., Smooth points of the unit ball of the space ( 2 l 1 ), Results Math., 36 (1999), 2633.

  • [7]

    Choi, Y. S. and Kim, S. G., Exposed points of the unit balls of the spaces p( 2 l p 2 ) ( p = 1 , 2 , ), Indian J. Pure Appl. Math., 35 (2004), 3741.

    • Search Google Scholar
    • Export Citation
  • [8]

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

  • [9]

    GÁMEZ-MERINO, J. L., MUÑOZ-FERNÁDEZ, G. A., SÁNCHEZ, V. M. and SEOANE-SEPÚlVEDA, J. B., Inequalities for polynomials on the unit square via the Krein–Milman Theorem, J. Convex Anal., 20(1) (2013), 125142.

    • Search Google Scholar
    • Export Citation
  • [10]

    Grecu, B. C., Geometry of three-homogeneous polynomials on real Hilbert spaces, J. Math. Anal. Appl., 246 (2000), 217229.

  • [11]

    Grecu, B. C., Smooth 2-homogeneous polynomials on Hilbert spaces, Arch. Math. (Basel), 76(6) (2001), 445454.

  • [12]

    Grecu, B. C., Geometry of 2-homogeneous polynomials on lp spaces, 1 < p < ∞, J. Math. Anal. Appl., 273 (2002), 262282.

  • [13]

    Grecu, B. C, Extreme 2-homogeneous polynomials on Hilbert spaces, Quaest. Math., 25(4) (2002), 421-435.

  • [14]

    GRECU, B. C., Geometry of homogeneous polynomials on two-dimensional real Hilbert spaces, J. Math. Anal. Appl., 293 (2004), 578-588.

  • [15]

    Grecu, B. C., MUÑOZ-FERÑNDEZ, G. A. and SEOANE-SEPÚLVEDA, J. B.., The unit ball of the complex P(3H), Math. Z., 263 (2009), 775-785.

  • [16]

    KIM S.G., Exposed 2-homogeneous polynomials on p( 2 l p 2 ) ( 1 p ), Math. Proc. R. Ir. Acad., 107 (2007), 123-129.

  • [17]

    KIM, S. G., The unit ball of s ( 2 l 2 ), Extracta Math., 24 (2009), 17-29.

  • [18]

    KIM, S. G., The unit ball of 𝒫(2d*(1,w)2), Math. Proc. R. Ir. Acad., 111(2) (2011), 79-94.

  • [19]

    KIM, S. G., The unit ball of 𝓛s(2 d*(1,w)2), Kyungpook Math. J., 53 (2013) 295306.

  • [20]

    KIM, S.G., Smooth polynomials of p( 2 d * ( 1 , w ) 2 ), Math. Proc. R. Ir. Acad., 113A(1) (2013), 45-58.

  • [21]

    KIM, S. G., Extreme bilinear forms of 𝓛(2d*(1,w)2), Kyungpook Math. J., 53 (2013), 625-638.

  • [22]

    KIM, S. G., Exposed symmetric bilinear forms of 𝓛s(2d*(1,w)2), Kyungpook Math. J., 54 (2014), 341-347.

  • [23]

    KIM, S. G., Polarization and unconditional constants of 𝒫(2d*(1,w)2), Commun. Korean Math. Soc, 29 (2014), 421-428.

  • [24]

    KIM, S. G., Exposed bilinear forms of 𝓛(2d*(1,w)2), Kyungpook Math. J., 55 (2015), 119-126.

  • [25]

    KIM, S. G., Exposed 2-homogeneous polynomials on the two-dimensional real pre- dual of Lorentz sequence space, Mediterr. J. Math., 13 (2016), 2827-2839.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [26]

    KIM, S. G., The unit ball of ( 2 h ( w ) 2 ), Bull. Korean Math. Soc, 54 (2017), 417428.

  • [27]

    KIM, S. G., Extremal problems for s ( 2 h ( w ) 2 ), Kyungpook Math. J., 57 (2017), 223-232.

  • [28]

    KIM, S. G., The unit ball of s ( 2 l 3 ), Comment. Math., 57 (2017), 1-7.

  • [29]

    KIM, S. G., The geometry of s ( 3 l 2 ), Commun. Korean Math. Soc, 32 (2017), 991-997.

  • [30]

    KIM, S. G., Extreme 2-homogeneous polynomials on the plane with a hexagonal norm and applications to the polarization and unconditional constants, Studia Set. Math. Hungar., 54 (2017), 362-393.

    • Search Google Scholar
    • Export Citation
  • [31]

    KIM, S. G., The geometry of ( 3 l 2 ) and optimal constants in the Bohnenblust- Hill inequality for multilinear forms and polynomials, Extracta Math., 33(1) (2018), 51-66.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [32]

    KIM, S. G., Extreme bilinear forms on ℝn with the supremum norm, Period. Math. Hungar., 77 (2018), 274-290.

  • [33]

    KIM, S. G., Exposed polynomials of p( 3 h ( 1 2 ) 2 ), Extracta Math., 33(2) (2018), 127– 143.

  • [34]

    KIM, S. G., Extreme and exposed multi-linear forms on ℝ2 with the supremum norm, preprint.

  • [35]

    KIM, S. H. and Lee, S. H., Exposed 2-homogeneous polynomials on Hilbert spaces, Proc. Amer. Math. Soc, 131 (2003), 449-453.

  • [36]

    Konheim, A. G. and RIVLIN, T. J., Extreme points of the unit ball in a space of real polynomials, Amer. Math. Monthly, 73 (1966), 505-507.

  • [37]

    MILEV, L. NAIDENOV, N., Strictly definite extreme points of the unit ball in a polynomial space, C R. Acad. Bulg. Sci., 61 (2008), 1393-1400.

    • Search Google Scholar
    • Export Citation
  • [38]

    MILEV, L. NAIDENOV, N., Indefinite extreme points of the unit ball in a polynomial space, Acta Sci. Math. (Szeged) 77(3-4) (2011), 409-424.

    • Search Google Scholar
    • Export Citation
  • [39]

    MILEV, L. NAIDENOV, N., Semidefinite extreme points of the unit ball in a polynomial space, J. Math. Anal. Appl., 405 (2013), 631-641.

  • [40]

    MUÑOZ-FERÑNDEZ, G. A.., Pellegrino, D., SEOANE-SEPÚLVEDA, J. B. and Weber, A., Supremum norms for 2-homogeneous polynomials on circle sectors, J. Convex Anal., 21(3) (2014), 745-764.

    • Search Google Scholar
    • Export Citation
  • [41]

    MUÑOZ-FERÑNDEZ, G. A.., RÉVÉSZ, S. G. and SEOANE-SEPÚLVEDA, J. B.., Geometry of homogeneous polynomials on non symmetric convex bodies, Math. Scand., 105 (2009), 147-160.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [42]

    MUÑOZ-FERÑNDEZ, G. A. and SEOANE-SEPÚLVEDA, J. B., Geometry of Banach spaces of trinomials, J. Math. Anal. Appl., 340 (2008), 1069-1087.

  • [43]

    NEUWIRTH, S., The maximum modulus of a trigonometric trinomial, J. Anal. Math., 104 (2008), 371-396.

  • [44]

    RÉVÉSZ, S. G., Minimization of maxima of nonnegative and positive definite cosine polynomials with prescribed first coefficients, Acta Sci. Math. (Szeged), 60(3-4) (1995), 589-608.

    • Search Google Scholar
    • Export Citation
  • [45]

    Ryan, R. A. and TURETT, B., Geometry of spaces of polynomials, J. Math. Anal. Appl., 221 (1998), 698-711.

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