Let X1 and X2 be complex Banach spaces with dimension at least three, A1 and A2 be standard operator algebras on X1 and X2, respectively. For k ≥ 2, let （i1, i2, . . . , im） be a finite sequence such that {i1, i2, ...Let X1 and X2 be complex Banach spaces with dimension at least three, A1 and A2 be standard operator algebras on X1 and X2, respectively. For k ≥ 2, let （i1, i2, . . . , im） be a finite sequence such that {i1, i2, . . . , im} = {1, 2, . . . , k} and assume that at least one of the terms in （i1, . . . , im） appears exactly once. Define the generalized Jordan productT1 o T2 o··· o Tk = Ti1Ti2··· Tim ＋ Tim··· Ti2Ti1 on elements in Ai. This includes the usual Jordan product A1A2 ＋ A2A1, and the Jordan triple A1A2A3 ＋ A3A2A1. Let Φ ： A1 → A2 be a map with range containing all operators of rank at most three. It is shown that Φ satisfies that σπ（Φ（A1） o··· o Φ（Ak）） = σπ（A1 o··· o Ak） for all A1, . . . , Ak, where σπ（A） stands for the peripheral spectrum of A, if and only if Φ is a Jordan isomorphism multiplied by an m-th root of unity.展开更多
Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple ...Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11171249,11101250,11271217)
文摘Let X1 and X2 be complex Banach spaces with dimension at least three, A1 and A2 be standard operator algebras on X1 and X2, respectively. For k ≥ 2, let （i1, i2, . . . , im） be a finite sequence such that {i1, i2, . . . , im} = {1, 2, . . . , k} and assume that at least one of the terms in （i1, . . . , im） appears exactly once. Define the generalized Jordan productT1 o T2 o··· o Tk = Ti1Ti2··· Tim ＋ Tim··· Ti2Ti1 on elements in Ai. This includes the usual Jordan product A1A2 ＋ A2A1, and the Jordan triple A1A2A3 ＋ A3A2A1. Let Φ ： A1 → A2 be a map with range containing all operators of rank at most three. It is shown that Φ satisfies that σπ（Φ（A1） o··· o Φ（Ak）） = σπ（A1 o··· o Ak） for all A1, . . . , Ak, where σπ（A） stands for the peripheral spectrum of A, if and only if Φ is a Jordan isomorphism multiplied by an m-th root of unity.
基金The NSF (10571114) of Chinathe Natural Science Basic Research Plan (2005A1) of Shaanxi Province of China
文摘Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices.
