A zk-invariant subspace without the wandering property Articles uri icon

publication date

  • April 2019

start page

  • 1377

end page

  • 1400

issue

  • 2

volume

  • 472

International Standard Serial Number (ISSN)

  • 0022-247X

Electronic International Standard Serial Number (EISSN)

  • 1096-0813

abstract

  • We study operators of multiplication by zk in Dirichlet-type spaces Dalfa. We establish the existence of k and alfa for which some zk-invariant subspaces of Dalfa do not satisfy the wandering property. As a consequence of the proof, any Dirichlet-type space accepts an equivalent norm under which the wandering property fails for some space for the operator of multiplication by zk, for any k≥6.

keywords

  • dirichlet spaces; wandering property; invariant subspaces; multiplication operators; shift operator; bergman spaces