scholarly journals The Invariant Subspace Problem for Non-Archimedean Banach Spaces

2008 ◽  
Vol 51 (4) ◽  
pp. 604-617 ◽  
Author(s):  
Wiesław Śliwa
Keyword(s):  
Banach Space ◽  
Invariant Subspace ◽  
Banach Spaces ◽  
Continuous Operator ◽  
Linear Continuous Operator ◽  
Infinite Dimensional ◽  
Countable Type ◽  
Closed Invariant Subspace ◽  
Subspace Problem ◽  
Invariant Subspace Problem

AbstractIt 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.

scholarly journals An invariant subspace theorem on subdecomposable operators

2000 ◽  
Vol 61 (1) ◽  
pp. 11-26
Author(s):  
Mingxue Liu
Keyword(s):  
Invariant Subspace ◽  
Additional Condition ◽  
Subspace Theorem ◽  
Subspace Problem ◽  
Invariant Subspace Problem

H. Mohebi and M. Radjabalipour raised a conjecture on the invariant subspace problem in 1994. In this paper, we prove the conjecture under an additional condition, and obtain an invariant subspace theorem on subdecomposable operators.

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