Decompositions of Banach lattices into direct sums

Casazza, P. G.; Kalton, N. J.; Tzafriri, L.

doi:10.1090/S0002-9947-1987-0911095-9

Decompositions of Banach lattices into direct sums
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by P. G. Casazza, N. J. Kalton and L. Tzafriri PDF

Trans. Amer. Math. Soc. 304 (1987), 771-800 Request permission

Abstract:

We consider the problem of decomposing a Banach lattice $Z$ as a direct sum $Z = X \oplus Y$ where $X$ and $Y$ are complemented subspaces satisfying a condition of incomparability (e.g. every operator from $Y$ to $X$ is strictly singular). We treat both the atomic and nonatomic cases. In particular we answer a question of Wojtaszczyk by showing that ${L_1} \oplus {L_2}$ has unique structure as a nonatomic Banach lattice.

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Some remarks concerning sign-embeddings

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