Bilocal derivations

of standard operator algebras

Authors:
Jun Zhu and Changping Xiong

Journal:
Proc. Amer. Math. Soc. **125** (1997), 1367-1370

MSC (1991):
Primary 47D30, 47D25, 47B47

DOI:
https://doi.org/10.1090/S0002-9939-97-03722-2

MathSciNet review:
1363442

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we shall show the following two results: (1) Let be a standard operator algebra with , if is a linear mapping on which satisfies that maps into for all , then is of the form for some in . (2) Let be a Hilbert space, if is a norm-continuous linear mapping on which satisfies that maps into for all self-adjoint projection in , then is of the form for some in .

**1.**M. Bresar,*Characterizations of derivations on some normed algebras with involution*, J. Algebra**152**(1992), 454-462. MR**94e:46098****2.**M. Bresar,*Jordan derivation on semiprime rings*, Proc. Amer. Math. Soc. (4)**104**(1988), 1003-1006. MR**89d:16004****3.**P. R. Chernoff,*Representations, automorphism and derivation of some operator algebras*, J. Funct. Anal.**12**(1973), 275-289. MR**50:2934****4.**R. Kadison,*Local derivation*, J. Algebra**130**(1990), 494-509. MR**91f:46092****5.**D. R. Larson and A. R. Sourour,*Local derivation and local automorphism of*, Proc. Sympos. Pure Math. (2)**51**(1990), 187-194. MR**91k:47106****6.**P. Semrl,*Additive derivation of some operator algebras*, Illinois J. Math. (2)**35**(1991), 234-240. MR**92b:47068**

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Additional Information

**Jun Zhu**

Affiliation:
Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei, 445000, People’s Republic of China

**Changping Xiong**

Affiliation:
Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei, 445000, People’s Republic of China

DOI:
https://doi.org/10.1090/S0002-9939-97-03722-2

Keywords:
Jordan derivation,
standard operator algebra,
bilocal derivation,
local derivation

Received by editor(s):
June 14, 1995

Received by editor(s) in revised form:
November 8, 1995

Additional Notes:
Project supported by the Science Foundation of HBEC, People’s Republic of China

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1997
American Mathematical Society