ABSTRACT

On the structure of strongly continuous one-parameter groups of multilinear functionals

L.L. STACHÓ

Out main results are structure theorems for strongly continuous one-parameter groups formed by surjective linear isometries of the space of bounded N-linear functionals over smoothly normed complex Banach spaces, in particular over Hilbert spaces. Though the Hilbert case with N = 1 factor is a natural analogue to Stone’s classical theorem, some crucial arguments of the proof go back to probability theory. As a consequence, we classify the strongly continuous one-parameter automorphism groups of all infinite-dimensional Cartan factors of Jordan theory. We reduce the investigation of the strongly continuous one-parameter groups by non-linear holomorphic automorphism of the unit ball in L(H, K) to the study of some retarded ordinary differential equations.