Abstract
Let \(L^{1}(G)\) and \(M(G)\) be the group algebra and the measure algebra of a locally compact group G, respectively, and \(\Delta :L^{1}(G)\rightarrow M(G)\) be a continuous linear map. Assuming that \(\Delta \) behaves like derivation or anti-derivation at orthogonal elements for several types of orthogonality conditions, our aim is to characterize such maps. Indeed, we assume that \(\Delta \) is a derivation or anti-derivation through orthogonality conditions on \(L^{1}(G)\) such as \(f*g=0\), \(f*g^{\star }=0\), \(f^{\star }*g=0\), \(f*g=g*f=0\) and \(f*g^{\star }=g^{\star }*f=0\).
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The author thanks the referee and Professor M. N. Ghosseiri for careful reading of the manuscript and for helpful suggestions.
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Ghahramani, H. Linear Maps on Group Algebras Determined by the Action of the Derivations or Anti-derivations on a Set of Orthogonal Elements. Results Math 73, 133 (2018). https://doi.org/10.1007/s00025-018-0898-2
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DOI: https://doi.org/10.1007/s00025-018-0898-2