期刊
MEDITERRANEAN JOURNAL OF MATHEMATICS
卷 14, 期 6, 页码 -出版社
SPRINGER BASEL AG
DOI: 10.1007/s00009-017-1032-5
关键词
Derivation; Hilbert C*-module; inner derivation; local derivation; 2-local derivation
资金
- National Natural Science Foundation of China [11371136]
For a commutative C*-algebra A with unit e and a Hilbert A-module M, denote by End(A)(M) the algebra of all bounded A-linear mappings on M, and by End*(A)(M) the algebra of all adjointable mappings onM. We prove that ifMis full, then each derivation on End(A)(M) is A-linear, continuous, and inner, and each 2-local derivation on EndA(M) or End*(A)(M) is a derivation. If there exist x(0) in M and f(0) in M', such that f(0)(x(0)) = e, where M' denotes the set of all bounded A-linear mappings fromMto A, then each A-linear local derivation on End(A)(M) is a derivation.
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