caa a22 4500 605461090 CHVBK 20210128100241.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10114-015-4367-5 doi (NATIONALLICENCE)springer-10.1007/s10114-015-4367-5 Maps preserving peripheral spectrum of generalized Jordan products of operators [Elektronische Daten] [Wen Zhang, Jin Hou, Xiao Qi] Let X 1 and X 2 be complex Banach spaces with dimension at least three, A 1 and A 2 be standard operator algebras on X 1 and X 2, respectively. For k ≥ 2, let (i 1, i 2,..., i m ) be a finite sequence such that {i 1, i 2,..., i m} = {1, 2,..., k} and assume that at least one of the terms in (i 1,..., i m) appears exactly once. Define the generalized Jordan product $${T_1} \circ {T_2} \circ \cdots \circ {T_k} = {T_{{i_1}}}{T_{{i_2}}} \cdots {T_{{i_m}}} + {T_{{i_m}}} \cdots {T_{{i_2}}}{T_{{i_1}}}$$ on elements in A i . This includes the usual Jordan product A 1 A 2 + A 2 A 1, and the Jordan triple A 1 A 2 A 3 + A 3 A 2 A 1. Let Φ: A 1 → A 2 be a map with range containing all operators of rank at most three. It is shown that Φ satisfies that σ π (Φ(A 1) ○ · · · ○ Φ(A k )) = σ π (A1 ○ ··· ○ A k ) for all A 1,..., A k , where σ π (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. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Peripheral spectrum nationallicence generalized Jordan products nationallicence Banach spaces nationallicence standard operator algebras nationallicence Zhang Wen Department of Mathematics, Shanxi University, 030006, Taiyuan, P. R. China aut Hou Jin Department of Mathematics, University of Technology, 030024, Taiyuan, P. R. China aut Qi Xiao Department of Mathematics, Shanxi University, 030006, Taiyuan, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/6(2015-06-01), 953-972 1439-8516 31:6<953 2015 31 10114 https://doi.org/10.1007/s10114-015-4367-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-4367-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zhang Wen Department of Mathematics, Shanxi University, 030006, Taiyuan, P. R. China aut NATIONALLICENCE 700 1- Hou Jin Department of Mathematics, University of Technology, 030024, Taiyuan, P. R. China aut NATIONALLICENCE 700 1- Qi Xiao Department of Mathematics, Shanxi University, 030006, Taiyuan, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/6(2015-06-01), 953-972 1439-8516 31:6<953 2015 31 10114