A KADEC-PELCZYNSKI DICHOTOMY-TYPE THEOREM FOR PREDUALS OF JBW*-ALGEBRAS

作者：Fernandez Polo Francisco J^*; Peralta Antonio M; Isabel Ramirez Maria

来源：Israel Journal of Mathematics, 2015, 208(1): 45-78.

DOI：10.1007/s11856-015-1193-5

We prove a Kadec-Pelczynski dichotomy-type theorem for bounded sequences in the predual of a JBW*-algebra, showing that for each bounded sequence (phi(n)) in the predual of a JBW*-algebra M, there exist a subsequence (phi(tau(n))), and a sequence of mutually orthogonal projections (p(n)) in M such that:
(a) the set {(phi(tau(n))) - phi(tau(n)) P-2 (p(n)) : n epsilon N} is relatively weakly compact,
(b) phi(tau(n)) =xi(n) + psi(n), with xi(n) := phi(tau(n)) - phi(tau(n)) -phi(tau(n)) P-2(p(n)) and psi(n) := phi(tau(n)) P-2 (p(n)), (xi nQ(p(n)) = 0 and psi(n)Q(pn)(2) = psi(n)), for every n.

• 出版日期2015-9