Generalized n-circular projections on JB*-triples

摘要

A nonzero projection Po on a complex Banach space X is said to be a generalized n-circular projection (n> 2) if there exist distinct modulus one complex numbers Ai,...,A_n_i, not equal to 1, and nonzero projections Pl,..., P_n-1 on X such that Po ? Pi ? . . . ? Pn-1 is the identity on X, and Po + λ1-P1 + . . . + λ_n_1P_n_1 is an isometry. If X is a JB*-triple and n = 2 then it is known that λ1= -1, or P0 and Pi are hermitian. The aim of this paper is to generalize this result for arbitrary n≥ 2, and to apply it to the case n= 3, that is, to the so-called generalized tricircular projections.