Korean J. Math.  Vol 24, No 3 (2016)  pp.397-407
DOI: https://doi.org/10.11568/kjm.2016.24.3.397

$k-$ denting points and $k-$ smoothness of Banach spaces

Suyalatu Wulede, Shaoqiang Shang, Wurina Bao

Abstract


In this paper, the concepts of $k-$smoothness, $k-$very smoothness and $k-$strongly smoothness of Banach spaces are dealt with together briefly by introducing three types $k-$denting point regarding different topology of conjugate spaces of Banach spaces. In addition, the characterization of first type $w^{\ast}-k$ denting point is described by using the slice of closed unit ball of conjugate spaces.

Keywords


$k$ denting points, $k$ smooth spaces, $k$ very smooth spaces, $k$ strongly smooth spaces, Banach spaces

Subject classification

46B09; 46B20

Sponsor(s)

This work was supported by the National Natural Science Foundation of China (Grant no.11561053) and Foundation of Inner Mongolia Normal University RCPY-2-2012-K-034.

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References


Ky Fan and I. Glicksburg, Fully convex normed linear spaces, Proc. Natl. Acad. Sci. USA 41 (1955), 947–953. (Google Scholar)

P.D.Liu, Martingle and Geometric of Banach Space. Science Press. Shanghai (in Chinese), 2007. (Google Scholar)

H.B.Maynard, A geometrical characterization of Banach spaces having the Radon-Nikodym property, Trans.Amer.Math.Soc. 185(1973) 493-500. (Google Scholar)

C.X.Nan and J.H.Wang, k-strict convexity and k-smoothness, Chinese Ann.Math (in Chinese).(Series A). 11(3)(1990) 321-324. (Google Scholar)

M.A.Rieffel, Dentable subsets of Banach spaces, with applications to a Radon-Nikodym theorem, Funct.Anal.Proc. (Conf. Irvine, Calif., 1966), Acad.Press,London,Thompson, Washington, D.C. 71-77. (Google Scholar)

S.Q.Shang,Y.A.Cui,Y.Q.Fu, Denting point, smoothness of Banach spaces and approximation compactness[J]. Acta Mathematica Sinica (in Chinese). 53(6)(2010) 1217-1224. (Google Scholar)

C.X.Wu, Y.J.Li, Strong convexity in Banach spaces,Chin.J.Math. 13(1993) 105- 108. (Google Scholar)

X.T. Yu. Geometric Theory of Banach Space.East China Normal Univ (in Chi- nese), 1984. (Google Scholar)

Z.H.Zhang On k-strictly convex and k-very smooth Banach space, North- east.Math.J. 12(2)(1996) 165-170. (Google Scholar)


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