Differentiability and ball-covering property in Banach spaces
A real Banach space is defined to have the ball-covering property if its unit sphere is contained in the union of countably many open balls that do not contain the origin. The main result of the paper is: The following two statements are equivalent for two Gâteaux differentiability spaces \(X\) and \(Y\): (1)~\(X\) and \(Y\) have the ball covering property. (2)~For some \(p\in [1,\infty]\), the product space (\(X\times Y, \|.\|_p)\) has the ball-covering property. (3)~For all \(p\in [1,\infty]\), the product space (\(X\times Y, \|.\|_p)\) has the ball-covering property.
scientific article; zbMATH DE number 6506796
scientific article