International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 29-32, Pages 1679-1701
doi:10.1155/S0161171204309270

On the Beurling algebras Aα+(𝔻)—derivations and extensions

Abstract

Based on a description of the squares of cofinite primary ideals of Aα+(𝔻), we prove the following results: for α≥1, there exists a derivation from Aα+(𝔻) into a finite-dimensional module such that this derivation is unbounded on every dense subalgebra; for m∈ℕ and α∈[m,m+1), every finite-dimensional extension of Aα+(𝔻) splits algebraically if and only if α≥m+1/2.