Abstract
We initiate a study of structural properties of the quotient algebra K (X)/A(X) of the compact-by-approximable operators on Banach spaces X failing the approximation property. Our main results and examples include the following: (i) there is a linear isomorphic embedding from c(0) into K (Z)/A(Z), where Z belongs to the class of Banach spaces constructed by Willis that have the metric compact approximation property but fail the approximation property, (ii) there is a linear isomorphic embedding from a nonseparable space c(0)(Gamma) into K (Z(FJ))/A(Z(FJ)), where Z(FJ) is a universal compact factorisation space arising from the work of Johnson and Figiel.
Original language | English |
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Journal | Journal of the Australian Mathematical Society |
Volume | 110 |
Issue number | 2 |
Pages (from-to) | 266-288 |
Number of pages | 23 |
ISSN | 1446-7887 |
DOIs | |
Publication status | Published - Apr 2021 |
MoE publication type | A1 Journal article-refereed |
Fields of Science
- 111 Mathematics
- quotient algebra
- compact-by-approximable operators
- approximation properties