Geodesic
The Invariant Subspace Problem for Non-Archimedean Banach Spaces
Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 604-617

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DOI

It is proved that every infinite-dimensional non-archimedean Banach space of countable type admits a linear continuous operator without a non-trivial closed invariant subspace. This solves a problem stated by A. C. M. van Rooij and W. H. Schikhof in 1992.
DOI : 10.4153/CMB-2008-060-9
Mots-clés : 47S10, 46S10, 47A15, invariant subspaces, non-archimedean Banach spaces 
Śliwa, Wiesław. The Invariant Subspace Problem for Non-Archimedean Banach Spaces. Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 604-617. doi: 10.4153/CMB-2008-060-9
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     title = {The {Invariant} {Subspace} {Problem} for {Non-Archimedean} {Banach} {Spaces}},
     journal = {Canadian mathematical bulletin},
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     year = {2008},
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     number = {4},
     doi = {10.4153/CMB-2008-060-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-060-9/}
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