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ON λ-STRICT IDEALS IN BANACH SPACES
2010
Bulletin of the Australian Mathematical Society
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We define and study λ-strict ideals in Banach spaces, which for λ = 1 means strict ideals. Strict u-ideals in their biduals are known to have the unique ideal property; we prove that so also do λ-strict u-ideals in their biduals, at least for λ > 1/2. An open question, posed by Godefroy et al. ['Unconditional ideals in Banach spaces', Studia Math. 104 (1993), 13-59] is whether the Banach space X is a u-ideal in Ba(X ), the Baire-one functions in X * * , exactly when κ u (X ) = 1; we prove that
doi:10.1017/s0004972710001735
fatcat:4nbek3g3obb23cncfouvxcq4qm