## 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 |
---|---|

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