Abstract
AbstractWe show that every unconditional basis in a finite direct sum , with , splits into unconditional bases of each summand. This settles a 40 years old question raised in “A. Ortyński, Unconditional bases in , , Math. Nachr. 103 (1981), 109–116”. As an application we obtain that for any finite, the spaces , , and have a unique unconditional basis up to permutation.
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