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Based on a description of the squares of cofinite primary ideals of Aα+(), we prove the following results: for α≥1, there exists a derivation from Aα+() 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+() splits algebraically if and only if α≥m+1/2

international journal of mathematics and mathematical sciences

On the Beurling algebras<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$A_{\alpha}^+(\mathbb{D})$" id="E1"><mml:msubsup><mml:mi>A</mml:mi><mml:mi>α</mml:mi><mml:mo>+</mml:mo></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>𝔻</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>derivations and extensions

On the Beurling algebrasAα+(𝔻)derivations and extensions

On the Beurling algebrasAα+(𝔻)derivations and extensions