Abstract
We construct a reflexive and unconditionally saturated Banach space \( X_{uh} \) such that its dual \( X^{\ast}_{uh} \) is Hereditarily Indecomposable. We also show that every quotient of \( X_{uh} \) has a further quotient which is Hereditarily Indecomposable and every quotient of \( X^{\ast}_{uh} \) has a further quotient with an unconditional basis.
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Argyros, S., Tolias, A. Indecomposability and unconditionality in duality. Geom. funct. anal. 14, 247–282 (2004). https://doi.org/10.1007/s00039-004-0464-9
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DOI: https://doi.org/10.1007/s00039-004-0464-9