Multismoothness in Banach spaces
Summary: Motivated by the results published by \textit{R. Khalil} and \textit{A. Saleh} [Missouri J. Math. Sci. 17, No. 2, 76--87 (2005; Zbl 1085.46012)], we study the notion of \(k\)-smooth points and the notion of \(k\)-smoothness, which are dual to the notion of \(k\)-rotundity. Generalizing these notions and combining smoothness with the recently introduced notion of unitary, we study classes of Banach spaces for which the vector space, spanned by the state space corresponding to a unit vector, is a closed set.
scientific article; zbMATH DE number 5282538
scientific article