保持幂等算子乘积或约当三乘积非零幂等性的映射

J4 ›› 2010, Vol. 45 ›› Issue (12): 98-105.

保持幂等算子乘积或约当三乘积非零幂等性的映射

方莉¹,白维祖²

1.西北大学数学系, 陕西西安 710127; 2.甘肃科林电力设计有限责任公司, 甘肃兰州730050

收稿日期:2009-10-12 出版日期:2010-12-16 发布日期:2011-03-16

Maps preserving the idempotency of products or triple Jordan products of idempotent operators

FANG Li¹, BAI Wei-zu²

1. Department of Mathematics, Northwest University, Xi′an 710127, Shaanxi, China;
2. Colin Gansu Province Electric Power Design Co., Ltd., Lanzhou 730050, Gansu, China

Received:2009-10-12 Online:2010-12-16 Published:2011-03-16
About author:FANG Li(1978-), Female, Ph.D. candidate, Lecturer, her research mainly focuses on operator algebra and operator theory. Email: fangli@nwu.edu.cn
Supported by:
Supported by the Special Research Project of Educational Department of Shaanxi Province(No.09JK741) and the Research Start-up Foundation of Northwest University(No.JXL08PR09066)

摘要/Abstract

摘要：

设I(X)是复巴拿赫空间X上幂等算子之全体, 其中X的维数至少是3维。本文分别给出了I(X)上双边保持幂等算子乘积和约当三乘积非零幂等性的映射的具体结构形式。

关键词: 保持映射; 幂等算子; 幂等算子乘积

Abstract:

Let I(X) be the set of all idempotent operators on a complex Banach space X. The purpose of this note is to give the concrete form of either that every surjective map φ on I(X) such that AB is a nonzero idempotent if and only if φ(A)φ(B) is for all A,B∈I(X) or that every surjective map φ on I(X) such that ABA is a nonzero idempotent if and only if φ(A)φ(B)φ(A) is for all A,B∈I(X), when the dimension of X is at least 3.

Key words: preserver map; idempotent operator; products of idempotent operators

方莉1,白维祖2. 保持幂等算子乘积或约当三乘积非零幂等性的映射[J]. J4, 2010, 45(12): 98-105.

FANG Li1, BAI Wei-zu2. Maps preserving the idempotency of products or triple Jordan products of idempotent operators[J]. J4, 2010, 45(12): 98-105.

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