2021
DOI: 10.48550/arxiv.2105.08403
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Closed ideals in the algebra of compact-by-approximable operators

Hans-Olav Tylli,
Henrik Wirzenius

Abstract: We construct various examples of non-trivial closed ideals of the compact-byapproximable algebra AX =: K(X)/A(X) on Banach spaces X failing the approximation property. The examples include the following: (i) if X has cotype 2, Y has type 2, AX = {0} and AY = {0}, then AX⊕Y has at least 2 closed ideals, (ii) there are closed subspaces X ⊂ ℓ p for 4 < p < ∞ and X ⊂ c0 such that AX contains a non-trivial closed ideal, (iii) there is a Banach space Z such that AZ contains an uncountable lattice of closed ideal hav… Show more

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