Higher Derivations Associated with the Cauchy-Jensen Type Mapping

Subject Areas : Applied Mathematics

Majid Gordji ¹ , Hamidreza Reisi ²

1 - Department of Mathematics, Semnan University, Semnan, Iran.
2 - Department of Mathematics, Semnan University, Semnan, Iran

Received: 2016-02-15 Accepted : 2016-09-11 Published : 2018-12-01

Keywords: Cauchy--Jensen type higher derivation, Cauchy-Jensen type higher Jordan derivation, Approximate-strong, C*-algebra,

Abstract :

Let H be an innite dimensional Hilbert space and K(H) be the set of all compactoperators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate ofhigher derivation and higher Jordan derivation on K(H) associated with the following Cauchy-Jensentype functional equation 2f((T + S)/2+ R) = f(T ) + f(S) + 2f(R) for all T, S, R are in K(H).