In some work with systems of ordinary differential equations, a certain compact convex subset of a Banach space of vector-valued functions continuous on the real closed interval [0,l] was introduced [l]. The topology in this Banach space is induced by the supremum norm, while the norm used in the n-dimensional vector space of function values is arbitrary. It is observed in this note that all functions of this class have the same norm, a linear function on the set [0,l]. However, the nature of this subset depends rather markedly on the type of vector norm used.
Proceedings of the Iowa Academy of Science
©1962 Iowa Academy of Science, Inc.
"A Class of Vector Functions with Linear Norms,"
Proceedings of the Iowa Academy of Science, 69(1), 442-443.
Available at: https://scholarworks.uni.edu/pias/vol69/iss1/68