Vol. 64, No. 1, 1976

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Subsequences and rearrangements of sequences in FK spaces

Robert M. DeVos

Vol. 64 (1976), No. 1, 129–135

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 p contains all rearrangements of some sequence not in p, then it is a wedge space. This leads to proofs that if X is a solid symmetric FK space, Xpϕ, Xs, then XAp for any matrix A and if in addition X is not wedge then X and p are not linearly homeomorphic, via a matrix, hence extending a result of Banach.

Mathematical Subject Classification 2000
Primary: 40J05
Received: 8 September 1975
Revised: 30 March 1976
Published: 1 May 1976
Robert M. DeVos