PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2014 | 12 | 11 | 1700-1713
Tytuł artykułu

On the frame of the unit ball of Banach spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The notion of the frame of the unit ball of Banach spaces was introduced to construct a new calculation method for the Dunkl-Williams constant. In this paper, we characterize the frame of the unit ball by using k-extreme points and extreme points of the unit ball of two-dimensional subspaces. Furthermore, we show that the frame of the unit ball is always closed, and is connected if the dimension of the space is not less than three. As infinite dimensional examples, the frame of the unit balls of c 0 and ℓ p are determined.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
11
Strony
1700-1713
Opis fizyczny
Daty
wydano
2014-11-01
online
2014-06-29
Twórcy
Bibliografia
  • [1] Aizpuru A., García-Pacheco F. J., Some questions about rotundity and renormings in Banach spaces, J. Aust. Math. Soc., 2005, 79(1), 131–140 http://dx.doi.org/10.1017/S144678870000937X
  • [2] Aizpuru A., García-Pacheco F. J., A short note about exposed points in real Banach spaces, Acta Math. Sci. Ser. B Engl. Ed., 2008, 28(4), 797–800 http://dx.doi.org/10.1016/S0252-9602(08)60080-6
  • [3] Asplund E., A k-extreme point is the limit of k-exposed points, Israel J. Math., 1963, 1, 161–162 http://dx.doi.org/10.1007/BF02759703
  • [4] Birkhoff G., Orthogonality in linear metric spaces, Duke Math. J., 1935, 1(2), 169–172 http://dx.doi.org/10.1215/S0012-7094-35-00115-6
  • [5] Day M.M., Polygons circumscribed about closed convex curves, Trans. Amer. Math. Soc., 1947, 62, 315–319 http://dx.doi.org/10.1090/S0002-9947-1947-0022686-9
  • [6] Day M.M., Some characterizations of inner-product spaces, Trans. Amer. Math. Soc., 1947, 62, 320–337 http://dx.doi.org/10.1090/S0002-9947-1947-0022312-9
  • [7] García-Pacheco F. J., On exposed faces and smoothness, Bull. Braz. Math. Soc. (N.S.), 2009, 40(2), 237–245 http://dx.doi.org/10.1007/s00574-009-0011-2
  • [8] García-Pacheco F. J., On minimal exposed faces, Ark. Mat., 2011, 49(2), 325–333 http://dx.doi.org/10.1007/s11512-010-0123-3
  • [9] James R.C., Orthogonality in normed linear spaces, Duke Math. J., 1945, 12, 291–302 http://dx.doi.org/10.1215/S0012-7094-45-01223-3
  • [10] James R.C., Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc., 1947, 61, 265–292 http://dx.doi.org/10.1090/S0002-9947-1947-0021241-4
  • [11] James R.C., Inner products in normed linear spaces, Bull. Amer. Math. Soc., 1947, 53, 559–566 http://dx.doi.org/10.1090/S0002-9904-1947-08831-5
  • [12] Kato M., Saito K.-S., Tamura T., Sharp triangle inequality and its reverse in Banach spaces, Math. Inequal. Appl., 2007, 10(2), 451–460
  • [13] Liu Z., Zhuang Y.D., K-rotund complex normed linear spaces, J. Math. Anal. Appl., 1990, 146(2), 540–545 http://dx.doi.org/10.1016/0022-247X(90)90323-8
  • [14] Megginson R.E., An Introduction to Banach Space Theory, Springer-Verlag, New York, 1998 http://dx.doi.org/10.1007/978-1-4612-0603-3
  • [15] Mizuguchi H., Saito K.-S., Tanaka R., On the calculation of the Dunkl-Williams constant of normed linear spaces, Cent. Eur. J. Math., 2013, 11(7), 1212–1227. http://dx.doi.org/10.2478/s11533-013-0238-4
  • [16] Singer I., On the set of the best approximations of an element in a normed linear space, Rev. Math. Pures. Appl., 1960, 5, 383–402
  • [17] Singer I., Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer-Verlag, New York-Berlin, 1970 http://dx.doi.org/10.1007/978-3-662-41583-2
  • [18] Zhuang Y.D., On k-rotund complex normed linear spaces, J. Math. Anal. Appl., 1993, 174(1), 218–230 http://dx.doi.org/10.1006/jmaa.1993.1112
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0437-7
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.