Type and cotype in vector-valued Nakano sequence spaces

[摘要] Given a sequence of Banach spaces {X-n}(n) and a sequence of real numbers {p(n)}(n) in [1, infinity), the vector-valued Nakano sequence spaces l({p(n)}, {X-n}) consist of elements {x(n)}(n) in Pi(n)X(n) for which there is a constant lambda > 0 such that Sigma(n)(parallel tox(n)parallel to/lambda)(pn) < infinity. In this paper we find the conditions on the Banach spaces X-n and on the sequence {p(n)}(n) for the spaces l({p(n)}, {X-n}) to have cotype q or type p. (C) 2001 Elsevier Science.

[发布日期] 2001-12-15

[关键词] type;cotype;nakano sequence space