The lambda-function in the space P((2)l(2)(2))

Abstract

In this note, motivated by the question 1 in (Aron and Lohman, Pacific J. Math. 127 (1987), 209-231), we obtain an explicit formula for the lambda-function in the real space P((2)l(2)(2)). From this we see that the X-function is continuous and attained at each point of the unit ball of P((2)l(2)(2)), the space of real-valued continuous 2-homogeneous polynomials on l(2)(2).