The purpose of this paper is
to study FK spaces which contain all subsequences or all rearrangements of a given
sequence. Using a result of Bennett and Kalton we are able to show that if a
separable FK space contains all subsequences or all rearrangements of a sequence
with two or more finite cluster points, then it contains m. We are also able to show
that if ℓp contains all rearrangements of some sequence not in ℓp, then it is a wedge
space. This leads to proofs that if X is a solid symmetric FK space, X∖ℓp≠ϕ, X≠s,
then X≠ℓAp for any matrix A and if in addition X is not wedge then X and ℓp
are not linearly homeomorphic, via a matrix, hence extending a result of
Banach.
