Extreme and exposed points of L(^n l^2_∞ ) and L_s (^n l^2_∞)
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Abstract
For every n ≥ 2 this paper is devoted to the description of the sets of extreme and exposed points of the closed unit balls of L(n l2∞ ) and Ls(n l2∞ ), where L(n l2∞ ) is the space of n-linear forms on R2 with the supremum norm, and Ls(n l2∞ ) is the subspace of L(n l2∞ ) consisting of symmetric n-linear forms. First we classify the extreme points of the closed unit balls of L(n l2∞ ) and Ls(n l2∞ ) correspondingly. As corollaries we obtain |ext BL(n l2∞ ) | = 2(2n) and =|ext BLs(n l2∞ ) | =2n+1. We also show that exp BL(n l2∞ ) =ext BL(n l2∞ ) and exp BLs(n l2∞ ) =ext BLs(n l2∞ ) .
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How to Cite
Kim, S. G. (2020). Extreme and exposed points of L(^n l^2_∞ ) and L_s (^n l^2_∞). Extracta Mathematicae, 35(2), 127-135. Retrieved from https://publicaciones.unex.es/index.php/EM/article/view/2605-5686.35.2.127
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Banach Spaces and Operator Theory
References
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[2] S.G. Kim, The unit ball of Ls (2 d∗(1, w)2 ), Kyungpook Math. J. 53 (2013), 295 – 306.
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[6] S.G. Kim, The unit ball of L(2 Rh(w) 2 ), Bull. Korean Math. Soc. 54 (2017), 417 – 428.
[7] S.G. Kim, Extremal problems for Ls(2 Rh(w) 2 ), Kyungpook Math. J. 57 (2017), 223 – 232.
[8] S.G. Kim, The unit ball of Ls (2l∞ 3), Comment. Math. 57 (2017), 1 – 7.
[9] S.G. Kim, The geometry of Ls(3 l∞ 2), Commun. Korean Math. Soc. 32 (2017), 991 – 997.
[10] S.G. Kim, The geometry of L(3 l∞ 2) and optimal constants in the Bohnenblust-Hill inequality for multilinear forms and polynomials, Extracta Math. 33 (1) (2018), 51 – 66.
[11] S.G. Kim, Extreme bilinear forms on Rn with the supremum norm, Period. Math. Hungar. 77 (2018), 274 – 290.
[12] S.G. Kim, The unit ball of the space of bilinear forms on R3 with the supremum norm, Commun. Korean Math. Soc. 34 (2) (2019), 487 – 494.
[13] M.G. Krein, D.P. Milman, On extreme points of regular convex sets, Studia Math. 9 (1940), 133 – 137.
[2] S.G. Kim, The unit ball of Ls (2 d∗(1, w)2 ), Kyungpook Math. J. 53 (2013), 295 – 306.
[3] S.G. Kim, Extreme bilinear forms of L(2d∗ (1, w)2), Kyungpook Math. J. 53 (2013), 625 – 638.
[4] S.G. Kim, Exposed symmetric bilinear forms of Ls(2 d∗(1, w)2 ), Kyungpook Math. J. 54 (2014), 341 – 347.
[5] S.G. Kim, Exposed bilinear forms of L(2 d∗ (1, w)2 ), Kyungpook Math. J. 55 (2015), 119 – 126.
[6] S.G. Kim, The unit ball of L(2 Rh(w) 2 ), Bull. Korean Math. Soc. 54 (2017), 417 – 428.
[7] S.G. Kim, Extremal problems for Ls(2 Rh(w) 2 ), Kyungpook Math. J. 57 (2017), 223 – 232.
[8] S.G. Kim, The unit ball of Ls (2l∞ 3), Comment. Math. 57 (2017), 1 – 7.
[9] S.G. Kim, The geometry of Ls(3 l∞ 2), Commun. Korean Math. Soc. 32 (2017), 991 – 997.
[10] S.G. Kim, The geometry of L(3 l∞ 2) and optimal constants in the Bohnenblust-Hill inequality for multilinear forms and polynomials, Extracta Math. 33 (1) (2018), 51 – 66.
[11] S.G. Kim, Extreme bilinear forms on Rn with the supremum norm, Period. Math. Hungar. 77 (2018), 274 – 290.
[12] S.G. Kim, The unit ball of the space of bilinear forms on R3 with the supremum norm, Commun. Korean Math. Soc. 34 (2) (2019), 487 – 494.
[13] M.G. Krein, D.P. Milman, On extreme points of regular convex sets, Studia Math. 9 (1940), 133 – 137.