International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 32, Pages 1679-1701
doi:10.1155/S0161171204309270
On the Beurling algebras Aα+(𝔻)—derivations and extensions
Fachbereich Mathematik-Informatik, Gesamthochschule Paderborn, Paderborn 33095, Germany
Received 27 September 2003
Copyright © 2004 Holger Steiniger. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.