= Pełczyński decomposition method
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For a <Banach space> $E$ satisfying $E\cong(\bigoplus_{n\ge1}E)_p$, a <complemented subspace> $W$ is absorbed by $E$: write $E\cong W\oplus V$, expand the countable sum, and absorb one additional copy of $W$ into the countably many $W$ summands. Hence $E\oplus W\cong E$. If $Z$ is complemented in $E$ and contains a complemented copy of $E$, write $Z\cong E\oplus W$ with $W$ complemented in $E$; the preceding argument gives $Z\cong E$. The decompositions are <Banach space isomorphisms>, not merely algebraic decompositions.
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