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

RUC systems in rearrangement invariant spaces

P. G. Dodds, E. M. Semenov, F. A. Sukochev (2002)

Studia Mathematica


We present necessary and sufficient conditions for a rearrangement invariant function space to have a complete orthonormal uniformly bounded RUC system.

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 < .

Infinite dimensional linear groups with many G - invariant subspaces

Leonid Kurdachenko, Alexey Sadovnichenko, Igor Subbotin (2010)

Open Mathematics


Let F be a field, A be a vector space over F, GL(F, A) be the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dim F(B/Core G(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char F.