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Search: MSC category 47S10 ( Operator theory over fields other than ${\bf R}$, ${\bf C}$ or the quaternions; non-Archimedean operator theory )

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1. CMB 2008 (vol 51 pp. 604)

{\'S}liwa, Wies{\l}aw
The Invariant Subspace Problem for Non-Archimedean Banach Spaces
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.

Keywords:invariant subspaces, non-archimedean Banach spaces
Categories:47S10, 46S10, 47A15

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