A note on convergence in Banach spaces of cotype p
Authors:
Xiang Chen Wang
Affiliation:
Department of Mathematics, Jilin University, Changchun, China
Department of Statistics, North Dakota State University, Fargo, ND 58105, USA
Abstract:
Let B be a separable Banach space. The following is one of the results proved in this paper. The Banach space B is of cotype p if and only if
1. dn, n 1, has no subsequence converging in probability, and
2. ∑n 1|an|p < ∞ whenever ∑n 1andn converges almost surely are equivalent for every sequence dn, n 1, of symmetric independent random elements taking values in B.
Author Keywords: Bounded in probability; convergence in probability; cotype; uniform tightness condition