Closed ideals in the algebra of compact-by-approximable operators

Closed ideals in the algebra of compact-by-approximable operators

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, (...

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Veröffentlicht in:Journal of functional analysis 2022-02, Vol.282 (4), p.109328, Article 109328
Hauptverfasser: Tylli, Hans-Olav, Wirzenius, Henrik
Format: Artikel
Sprache:eng
Schlagworte:
Approximation properties
Closed ideals
Compact-by-approximable operators
Quotient algebra
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Zusammenfassung: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
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2021.109328