CHARACTERIZATIONS OF GEOMETRICAL PROPERTIES OF BANACH SPACES USING ψ-DIRECT SUMS
CHARACTERIZATIONS OF GEOMETRICAL PROPERTIES OF BANACH SPACES USING ψ-DIRECT SUMS
Let X be a Banach space and <TEX>${\psi}$</TEX> a continuous convex function on <TEX>${\Delta}_{K+1}$</TEX> satisfying certain conditions. Let <TEX>$(X{\bigoplus}X{\bigoplus}{\cdots}{\bigoplus}X)_{\psi}$</TEX> be the <TEX>${\psi}$</TEX>-direct sum of X. In this paper, we characterize the K strict convexity, K uniform convexity and uniform non-<TEX>$l^N_1$</TEX>-ness of Banach spaces using <TEX>${\psi}$</TEX>-direct sums.