## Abstract

Let E, F be either Fréchet or complete DF-spaces and let A(E, F) ⊆ B(E, F) be spaces of operators. Under some quite general assumptions we show that: (i) A(E, F) contains a copy of c_{0} if and only if it contains a copy of l_{∞}; (ii) if c_{0} ⊆ A(E, F), then A(E, F) is complemented in B(E, F) if and only if A(E, F) = B(E, F); (iii) if E or F has an unconditional basis and A(E, F) ≠ L(E, F), then A(E, F) ⊇ c_{0}. The above results cover cases of many clssical operator spaces A. We show also that EεF contains l_{∞} if and only if E or F contains l_{∞}.

Original language | English |
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Pages (from-to) | 250-269 |

Number of pages | 20 |

Journal | Results in Mathematics |

Volume | 28 |

Issue number | 3 |

DOIs | |

Publication status | Published - Nov 1995 |

MoE publication type | A1 Journal article-refereed |

## Keywords

- 46A04
- 46A11
- 46A32
- 46A45
- c
- Fréchet spaces
- l
- Montel operators
- reflexive operators
- uncomplemented subspaces

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