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- W2068331977 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." @default.
- W2068331977 created "2016-06-24" @default.
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- W2068331977 date "2010-01-01" @default.
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- W2068331977 title "Annihilator-preserving maps, multipliers, and derivations" @default.
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- W2068331977 doi "https://doi.org/10.1016/j.laa.2009.06.002" @default.
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