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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.
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참고문헌 (9)
참고문헌 신청
Ky Fan / 1955 / Fully convex normed linear spaces / Proc. Natl. Acad. Sci. USA 41:947~953
P.D.Liu / 2007 / Martingle and Geometric of Banach Space / Science Press
H.B.Maynard / 1973 / A geometrical characterization of Banach spaces having the Radon-Nikodym property / Trans.Amer.Math.Soc 185:493~500
C.X.Nan / 1990 / k-strict convexity and k-smoothness / Chinese Ann.Math(Series A) 11(3):321~324
M.A.Riefiel / 1966 / Dentable subsets of Banach spaces, with applications to a Radon-Nikodym theorem / Funct.Anal.Proc. (Conf. Irvine, Calif., 1966) :71~77
P.D.Liu / 2007 / Martingle and Geometric of Banach Space / Science Press
H.B.Maynard / 1973 / A geometrical characterization of Banach spaces having the Radon-Nikodym property / Trans.Amer.Math.Soc 185:493~500
C.X.Nan / 1990 / k-strict convexity and k-smoothness / Chinese Ann.Math(Series A) 11(3):321~324
M.A.Riefiel / 1966 / Dentable subsets of Banach spaces, with applications to a Radon-Nikodym theorem / Funct.Anal.Proc. (Conf. Irvine, Calif., 1966) :71~77
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