Splittings of Banach spaces induced by Clifford algebras

N. L. Carothers, S. J. Dilworth, David Sobecki
1999 Proceedings of the American Mathematical Society  
Let H be an infinite-dimensional Hilbert space of density character m. By representing H as a module over an appropriate Clifford algebra, it is proved that H possesses a family {Aα}α∈m of proper closed nonzero subspaces such that Analogous results are proved for Lp spaces and for c 0 (X) and p(X) (1 ≤ p ≤ ∞) when X is an arbitrary nonzero Banach space.
doi:10.1090/s0002-9939-99-05374-5 fatcat:zzat6hzi5nfwlmx3h54xv6uyiq