Invariant subspaces for positive operators on Banach spaces with unconditional basis Articles uri icon

publication date

  • June 2022

start page

  • 5231

end page

  • 5242


  • 12


  • 150

International Standard Serial Number (ISSN)

  • 0002-9939

Electronic International Standard Serial Number (EISSN)

  • 1088-6826


  • We prove that every lattice homomorphism acting on a Banach space X with the lattice structure given by an unconditional basis has a nontrivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal, which is no longer true for every positive operator on such a space.
    Motivated by these examples, we characterize tridiagonal positive operators without non-trivial closed invariant ideals on X extending to this context a result of Grivaux on the existence of non-trivial closed invariant subspaces for tridiagonal operators.


  • Mathematics