본문 바로가기
KERD
논문KCI 등재

Extreme Points, Exposed Points and Smooth Points of the Space Ls(2l3∞)

김성권
경북대학교 자연과학대학 수학과|2020.09|Kyungpook Mathematical Journal|제60권 제3호|pp. 485-505|DOI 10.5666/KMJ.2020.60.3.485

1

조회

0

다운로드

1

인용

0

참고문헌

키워드

extreme pointsexposed pointssmooth points
주제분류수학

초록

We present a complete description of all the extreme points of the unit ball of Ls(2l31) which leads to a complete formula for kfk for every f 2 Ls(2l31)*. We also show that extBLs(2l31)  extBLs(2ln1) for every n  4: Using the formula for kfk for every f 2 Ls(2l31)*. we show that every extreme point of the unit ball of Ls(2l31) is exposed. We also characterize all the smooth points of the unit ball of Ls(2l31).

Abstract

We present a complete description of all the extreme points of the unit ball of Ls(2l31) which leads to a complete formula for kfk for every f 2 Ls(2l31)*. We also show that extBLs(2l31)  extBLs(2ln1) for every n  4: Using the formula for kfk for every f 2 Ls(2l31)*. we show that every extreme point of the unit ball of Ls(2l31) is exposed. We also characterize all the smooth points of the unit ball of Ls(2l31).

참고문헌 (32)

  1. R. M. Aron, "Local properties of polynomials on a Banach space", Illinois J. Math, 45, pp.25~39 (2001)
  2. Y. S. Choi, "Extreme polynomials and multilinear forms on l1", J. Math. Anal. Appl, 228, pp.467~482 (1998)
  3. Y. S. Choi, "The unit ball of P2(l 22)", Arch. Math. (Basel), 71, pp.472~480 (1998)
  4. Y. S. Choi, "Extreme polynomials on c0", Indian J. Pure Appl. Math, 29, pp.983~989 (1998)
  5. Y. S. Choi, "Smooth points of the unit ball of the space P(2l1)", Results Math, 36, pp.26~33 (1999)
  6. Y. S. Choi, "Exposed points of the unit balls of the spaces P(2l 2p) (p =1, 2, ∞)", Indian J. Pure Appl. Math., 35, pp.37~41 (2004)
  7. S. Dineen, "Complex analysis on infinite dimensional spaces" (1999), Springer-Verlag
  8. S. Dineen, "Extreme integral polynomials on a complex Banach space", Math. Scand, 92, pp.129~140 (2003)
  9. B. C. Grecu, "Geometry of 2-homogeneous polynomials on lp spaces, 1 < p < ∞", J. Math. Anal. Appl, 273, pp.262~282 (2002)
  10. B. C. Grecu, "Unconditional constants and polynomial inequalities", J. Approx. Theory, 161, pp.706~722 (2009)
  11. S. G. Kim, "Exposed 2-homogeneous polynomials on P(2l 2p) (1 ≤ p ≤ ∞)", Math. Proc. R. Ir. Acad., 107A, pp.123~129 (2007)
  12. S. G. Kim, "The unit ball of Ls(2l 2∞)", Extracta Math, 24, pp.17~29 (2009)
  13. S. G. Kim, "The unit ball of P(2d∗(1, w)2)", Math. Proc. R. Ir. Acad., 111A, pp.79~94 (2011)
  14. 김성권, "The Unit Ball of Ls(2d*(1,w)2)", Kyungpook Mathematical Journal, 53(2), pp.295~306 (2013), 경북대학교 자연과학대학 수학과[DOI]
  15. S. G. Kim, "Smooth polynomials of P(2d∗(1, w)2)", Math. Proc. R. Ir. Acad., 113A, pp.45~48 (2013)
  16. 김성권, "Extreme Bilinear Forms of L(2d*(1,w)2)", Kyungpook Mathematical Journal, 53(4), pp.625~638 (2013), 경북대학교 자연과학대학 수학과[DOI]
  17. 김성권, "Exposed Symmetric Bilinear Forms of Ls(2d*(1,w)2)", Kyungpook Mathematical Journal, 54(3), pp.341~347 (2014), 경북대학교 자연과학대학 수학과[DOI]
  18. 김성권, "Exposed Bilinear Forms of L(2d*(1,w)2)", Kyungpook Mathematical Journal, 55(1), pp.119~126 (2015), 경북대학교 자연과학대학 수학과[DOI]
  19. S. G. Kim, "Exposed 2-homogeneous polynomials on the two-dimensional real predual of Lorentz sequence space", Mediterr. J. Math, 13, pp.2827~2839 (2016)
  20. 김성근, "The unit ball of L(2R2h(w))", 대한수학회보, 54(2), pp.417~428 (2017), 대한수학회
  21. 김성권, "Extremal Problems for ${\mathcal L}_s(^2\mathbb{R}^2_{h(w)})$", Kyungpook Mathematical Journal, 57(2), pp.223~232 (2017), 경북대학교 자연과학대학 수학과
  22. S. G. Kim, "The unit ball of Ls(2l 3∞)", Comment. Math. Prace Mat, 57, pp.1~7 (2017)
  23. 김성권, "THE GEOMETRY OF Ls(3l2∞)", 대한수학회논문집, 32(4), pp.991~997 (2017), 대한수학회
  24. S. G. Kim, "The geometry of L(3l 2∞)and optimal constants in the Bohnenblust-Hille inequality for multilinear forms and polynomials", Extracta Math, 33(1), pp.51~66 (2018)
  25. S. G. Kim, "Extreme bilinear form on R n with the supremum norm", Period. Math. Hungar, 77, pp.274~290 (2018)
  26. S. G. Kim, "Exposed polynomials of P(2R 2h(12))", Extracta Math, 33(2), pp.127~143 (2018)
  27. Sung Guen Kim, "The unit ball of the space of bilinear forms on $\mathbb{R}^3$ with the supremum norm", 대한수학회논문집, 34(2), pp.487~494 (2019), 대한수학회[DOI]
  28. S. G. Kim, "Smooth polynomials of the space P(2R 2h(12))", ~
  29. S. G. Kim, "Exposed 2-homogeneous polynomials on Hilbert spaces", Proc. Amer. Math. Soc, 131, pp.449~453 (2003)
  30. G. A. Munoz-Fernandez, "Geometry of homogeneous polynomials on non symmetric convex bodies", Math. Scand, 105, pp.147~160 (2009)
  31. G. A. Munoz-Fernandez, "Geometry of Banach spaces of trinomials", J. Math. Anal. Appl, 340, pp.1069~1087 (2008)
  32. R. A. Ryan, "Geometry of spaces of polynomials", J. Math. Anal. Appl, 221, pp.698~711 (1998)

관련 논문AI추천

THE GEOMETRY OF Ls(3l2∞)김성권대한수학회 · 대한수학회논문집2017 · 제32권 제4호Extreme points of the space ${\mathcal L}(^2l_{\infty})$김성권대한수학회 · 대한수학회논문집2020 · 제35권 제3호The Geometry of L(2l_{infty}^2)김성근경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2018 · 제58권 제1호Smooth points of ${\mathcal L}_s(^nl_{\infty}^2)$김성권대한수학회 · 대한수학회보2020 · 제57권 제2호The unit ball of the space of bilinear forms on $\mathbb{R}^3$ with the supremum normSung Guen Kim대한수학회 · 대한수학회논문집2019 · 제34권 제2호The Unit Ball of Ls(2d*(1,w)2)김성권경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2013 · 제53권 제2호

이 간행물의 다른 논문 (14건)

Variants of Essential Arity for Partial FunctionsNareupanat Lekkoksung, Erkko Lehtonenpp. 423-443φ-prime Subsemimodules of Semimodules over Commutative SemiringsFatemeh Fatahi, Reza Safakishpp. 445-453Purities of Ordered Ideals of Ordered SemiringsPakorn Palakawong na Ayutthaya, Bundit Pibaljommeepp. 455-465On Diameter, Cyclomatic Number and Inverse Degree of Chemical GraphsReza Sharafdini, Ali Reza Ashrafi, Ali Ghalavandpp. 467-475On the Fekete-Szegö Problem for Starlike Functions of Complex OrderHanan Darwish, Abdel-Moniem Lashin, Bashar Al Saeedipp. 477-484
원문 보기