Motivated by recent studies on the strong diameter 2 property, we exhibit a simple reason why, in many direct sums of Banach spaces, the arithmetic mean of two slices may have diameter less than 2.
KHALIL, R. (1986). P-REPRESENTABLE OPERATORS IN BANACH SPACES. International Journal of Mathematics and Mathematical Sciences, 1986(), 653-658. https://doi.org/10.1155/S0161171286000819