The Invariant Subspace Problem for Non-Archimedean Banach Spaces

  title={The Invariant Subspace Problem for Non-Archimedean Banach Spaces},
  author={Wiesław Śliwa},
  journal={Canadian Mathematical Bulletin},
  pages={604 - 617}
  • W. Śliwa
  • Published 1 December 2008
  • Mathematics
  • Canadian Mathematical Bulletin
Abstract 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. 
3 Citations
Invariant subspace problem and compact operators on non-Archimedean Banach spaces
In this paper, the invariant Subspace Problem is studied for the class of non-Archimedean compact operators on an infinite-dimensional Banach space E over a nontrivial complete nonArchimedean valued


On the complemented subspaces problem
A Banach space is isomorphic to a Hilbert space provided every closed subspace is complemented. A conditionally σ-complete Banach lattice is isomorphic to anLp-space (1≤p<∞) or toc0(Γ) if every
On the invariant subspace problem for Banach spaces
© Séminaire analyse fonctionnelle (dit "Maurey-Schwartz") (École Polytechnique), 1975-1976, tous droits réservés. L’accès aux archives du séminaire d’analyse fonctionnelle implique l’accord avec les
A Solution to the Invariant Subspace Problem
An important open problem in operator theory is the invariant subspace problem. Since the problem is solved for all finite dimensional complex vector spaces of dimension at least 2, H denotes a
Non-Archimedean functional analysis
Topics in Functional Analysis over Valued Division Rings
Open problems
  • K. P. Hart
  • Computer Science
    Lambda-Calculus and Computer Science Theory
  • 1975
Non-Archimedean Functional Analysis. Monographs and Textbooks in Pure and Applied Math
  • 1978