Displaying similar documents to “Translation-invariant function algebras on abelian groups”

On invariant subspaces for polynomially bounded operators

Junfeng Liu (2017)

Czechoslovak Mathematical Journal


We discuss the invariant subspace problem of polynomially bounded operators on a Banach space and obtain an invariant subspace theorem for polynomially bounded operators. At the same time, we state two open problems, which are relative propositions of this invariant subspace theorem. By means of the two relative propositions (if they are true), together with the result of this paper and the result of C. Ambrozie and V. Müller (2004) one can obtain an important conclusion that every polynomially...

Invariant subspaces on multiply connected domains.

Ali Abkar, Hakan Hedenmalm (1998)

Publicacions Matemàtiques


The lattice of invariant subspaces of several Banach spaces of analytic functions on the unit disk, for example the Bergman spaces and the Dirichlet spaces, have been studied recently. A natural question is to what extent these investigations carry over to analogously defined spaces on an annulus. We consider this question in the context of general Banach spaces of analytic functions on finitely connected domains Ω­. The main result reads as follows: Assume that B is a Banach space of...

Reducible representations of abelian groups

Aharon Atzmon (2001)

Annales de l’institut Fourier


A criterion for reducibility of certain representations of abelian groups is established. Among the applications of this criterion, we give a positive answer to the translation invariant subspace problem for weighted L p spaces on locally compact abelian groups, for even weights and 1 < p < .