Characterizations of isomorphisms and derivations of some algebras |
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| Authors: | Jiankui Li Zhidong Pan |
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| Affiliation: | 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: | Let ? be a zero-product preserving bijective bounded linear map from a unital algebra A onto a unital algebra B such that ?(1)=k. We show that if A is a CSL algebra on a Hilbert space or a J-lattice algebra on a Banach space then there exists an isomorphism ψ from A onto B such that ?=kψ. For a nest algebra A in a factor von Neumann algebra, we characterize the linear maps on A such that δ(x)y+xδ(y)=0 for all x,y∈A with xy=0. |
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| Keywords: | Derivation Isomorphism Operator algebra Zero-product preserver |
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