Higher Derivations Associated with the Cauchy-Jensen Type Mapping

Subject Areas : Applied Mathematics

Hamidreza Reisi ¹ (Department of Mathematics, Semnan University, Semnan, Iran)

Received: 2015-10-23 Accepted : 2016-08-02 Published : 2017-05-01

Keywords:

Abstract :

Let H be aninfinite--dimensional Hilbert space and K(H) be the set of allcompact operators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher Jordan derivation on K(H) associated with the following cauchy-Jencen type functional equation 2f(\frac{T+S}{2}+R)=f(T)+f(S)+2f(R) for all T,S,R\in K(H).