The \(\lambda\)-function in the space \(P(^2\ell_2^2)\). (English) Zbl 0946.46039

Choi, Yun Sung; Kim, Sung Guen

J. Inequal. Appl. 3, No. 3, 303-311 (1999).

The \(\lambda\)-function for (the unit ball of) a Banach space is a certain quite specific function related to convexity and the extreme point structure [see R. H. Lohman, Contemp. Math. 85, 345-354 (1989; Zbl 0675.46006)]. The authors calculate the \(\lambda\)-function for the space of real-valued 2-homogeneous polynomials on the real space \(\ell^2\).

Reviewer: S.V.Kislyakov (St.Peterburg)

MSC:

46G25	(Spaces of) multilinear mappings, polynomials
46B20	Geometry and structure of normed linear spaces
46E15	Banach spaces of continuous, differentiable or analytic functions

Keywords:

extreme points; \(\lambda\)-property; convexity; extreme point structure; 2-homogeneous polynomials