On the Wandering Property in Dirichlet spaces Articles uri icon

publication date

  • April 2020

start page

  • 1

end page

  • 12

issue

  • 2

volume

  • 92

International Standard Serial Number (ISSN)

  • 0378-620X

abstract

  • We show that in a scale of weighted Dirichlet spaces Dalfa, including the Bergman space, given any finite Blaschke product B there exists an equivalent norm in Dalfa such that B satisfies the wandering subspace property with respect to such norm. This extends, in some sense, previous results by Carswell et al. (Indiana Univ Math J 51(4):931-961, 2002). As a particular instance, when B(z)=zk and |alfa|≤log(2)log(k+1), the chosen norm is the usual one in Dalfa.

subjects

  • Mathematics

keywords

  • blaschke products; dirichlet spaces; renorming; shift operators; wandering subspace property