Annihilator-preserving maps, multipliers, and derivations |
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Authors: | Jiankui Li |
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Institution: | a Department of Mathematics, East China University of Science and Technology, Shanghai 200237, PR China b Department of Mathematics, Saginaw Valley State University, University Center, MI 48710, USA |
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Abstract: | For a commutative subspace lattice L in a von Neumann algebra N and a bounded linear map f:N∩algL→B(H), we show that if Af(B)C=0 for all A,B,C∈N∩algL satisfying AB=BC=0, then f is a generalized derivation. For a unital C∗-algebra A, a unital Banach A-bimodule M, and a bounded linear map f:A→M, we prove that if f(A)B=0 for all A,B∈A with AB=0, then f is a left multiplier; as a consequence, every bounded local derivation from a C∗-algebra to a Banach A-bimodule is a derivation. We also show that every local derivation on a semisimple free semigroupoid algebra is a derivation and every local multiplier on a free semigroupoid algebra is a multiplier. |
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Keywords: | Primary 47B47 47L35 |
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