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Jiménez Sevilla, María del Mar and Lajara, Sebastián
(2022)
*Operator ranges and endomorphisms with a prescribed behaviour on Banach spaces.*
(Unpublished)

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## Abstract

We obtain several extensions of a theorem of Shevchik which asserts that if R is a proper dense operator range in a separable Banach space E, then there exists a compact, one-to-one and dense-range operator T : E → E such that T(E) ∩ R = {0}, and some results of Chalendar and Partington concerning the existence of compact, one-to-one and dense-range endomorphisms on a separable Banach space E which leave invariant a given closed subspace Y ⊂ E, or more generally, a countable increasing chain of closed subspaces of E.

Item Type: | Article |
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Uncontrolled Keywords: | Separable Banach spaces; Nuclear operators; Operator ranges; Invariant subspaces; Chains of subspaces |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 75378 |

Deposited On: | 04 Nov 2022 18:10 |

Last Modified: | 07 Nov 2022 07:34 |

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