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- W3216281694 abstract "We construct various examples of non-trivial closed ideals of the compact-by-approximable 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⊂ℓp 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 ideals having the reverse order structure of the power set of the natural numbers. Some of our results involve non-classical approximation properties associated to various Banach operator ideals. We also discuss the existence of compact non-approximable operators X→Y, where X⊂ℓp and Y⊂ℓq are closed subspaces for p≠q." @default.
- W3216281694 created "2021-12-06" @default.
- W3216281694 creator A5040144799 @default.
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- W3216281694 date "2022-02-01" @default.
- W3216281694 modified "2023-09-25" @default.
- W3216281694 title "Closed ideals in the algebra of compact-by-approximable operators" @default.
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- W3216281694 doi "https://doi.org/10.1016/j.jfa.2021.109328" @default.
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