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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Decompositions of Banach lattices into direct sums


Authors: P. G. Casazza, N. J. Kalton and L. Tzafriri
Journal: Trans. Amer. Math. Soc. 304 (1987), 771-800
MSC: Primary 46B30
DOI: https://doi.org/10.1090/S0002-9947-1987-0911095-9
MathSciNet review: 911095
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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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DOI: https://doi.org/10.1090/S0002-9947-1987-0911095-9
Article copyright: © Copyright 1987 American Mathematical Society