JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (12): 1-4.doi: 10.6040/j.issn.1671-9352.0.2014.460

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A local characterization of centralizers on B(H)

YANG Yuan, ZHANG Jian-hua   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, Shaaxi, China
  • Received:2014-10-20 Revised:2015-01-26 Online:2015-12-20 Published:2015-12-23

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Abstract: Let H be a Hilbert space over the real or complex field F. Suppose Ф:B(H)→B(H) is a linear map such that 2Ф(P)=PФ(P)+Ф(P)P holds for all idempotent operators P∈B(H), then there exists a λ∈F such that Ф(A)=λA for all A∈B(H).

Key words: idempotent operator, centralizer, linear map

CLC Number: 

  • O177.1
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