DERIVATIONS ON CONVOLUTION ALGEBRAS
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In this paper, we investigate derivations on the noncommutative Banach algebra L∞ 0 (ω)∗ equipped with an Arens product. As a main result, we prove the Singer-Wermer conjecture for the noncommutative Banach algebra L∞ 0 (ω)∗. We then show that a derivation on L∞ 0 (ω)∗ is continuous if and only if its restriction to rad(L∞ 0 (ω)∗) is continuous. We also prove that there is no nonzero centralizing derivation on L∞ 0 (ω)∗. Finally, we prove that the space of all inner derivations of L∞ 0 (ω)∗ is continuously homomorphic to the space L∞ 0 (ω)∗/L1(ω).
Abstract
In this paper, we investigate derivations on the noncommutative Banach algebra L∞ 0 (ω)∗ equipped with an Arens product. As a main result, we prove the Singer-Wermer conjecture for the noncommutative Banach algebra L∞ 0 (ω)∗. We then show that a derivation on L∞ 0 (ω)∗ is continuous if and only if its restriction to rad(L∞ 0 (ω)∗) is continuous. We also prove that there is no nonzero centralizing derivation on L∞ 0 (ω)∗. Finally, we prove that the space of all inner derivations of L∞ 0 (ω)∗ is continuously homomorphic to the space L∞ 0 (ω)∗/L1(ω).
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