JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (12): 46-49.doi: 10.6040/j.issn.1671-9352.0.2019.391

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Strong new product preserving maps on *-algebras

ZHANG Fang-juan   

  1. School of Science, Xian University of Posts and Telecommunications, Xian 710121, Shaanxi, China
  • Published:2019-12-11

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Abstract: Let R be a unital *-algebra with a nontrivial symmetric idempotent P which satisfies:(1)ARP={0} implies A=0;(2)AR(I-P)={0} implies A=0. Let φ:R→R be a surjective map. Then φ is strong new product preserving if and only if there exists an element Z∈ZS(R)with Z2=I such that φ(X)=ZX for all X∈R. As an application, a characterization of strong new product preserving on von Neumann algebras with no central summands of type I1 and prime *-ring are obtained.

Key words: new product, preserving map, *-algebra

CLC Number: 

  • O177.1
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