Search results for "nakano sequence space"

Type and Cotype in Vector-Valued Nakano Sequence Spaces

2001

AbstractGiven a sequence of Banach spaces {Xn}n and a sequence of real numbers {pn}n in [1,∞), the vector-valued Nakano sequence spaces ℓ({pn},{Xn}) consist of elements {xn}n in ∏nXn for which there is a constant λ>0 such that ∑n(‖xn‖/λ)pn<∞. In this paper we find the conditions on the Banach spaces Xn and on the sequence {pn}n for the spaces ℓ({pn},{Xn}) to have cotype q or type p.