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Multiplicative mappings at some points on matrix algebras

โœ Scribed by Jun Zhu; Changping Xiong; Hong Zhu


Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
207 KB
Volume
433
Category
Article
ISSN
0024-3795

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Let L be a J-subspace lattice on a real or complex Banach space X with dim X > 2 and AlgL be the associated J-subspace lattice algebra. Let ฮด : AlgL โ†’ AlgL be an additive map. It is shown that, if ฮด is derivable at zero point, i.e., ฮด(AB) = ฮด(A)B + Aฮด(B) whenever AB = 0, then ฮด(A) = ฯ„ (A) + ฮปA, โˆ€A,

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Let A be a subalgebra with the unit operator I in B(H ), we say that a linear mapping ฯ• from A into B(H ) is a generalized derivable mapping at zero point if ฯ•(ST ) = ฯ•(S)T + Sฯ•(T ) -Sฯ•(I )T for any S, T โˆˆ A with ST = 0. In this paper, we show the following main result: every norm-continuous general

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โœ Gregor Dolinar ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 115 KB

Let M n be the algebra of all n ร— n complex matrices and P n the set of all idempotents in M n . Suppose ฯ† : M n โ†’ M n is a surjective map satisfying A -ฮปB โˆˆ P n if and only if