Higher Derivations Associated with the Cauchy-Jensen Type Mapping

Abstract

Let H be an infinite--dimensional Hilbert space and K(H) be the set of all compact 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<br /> <br />2f(frac{T+S}{2}+R)=f(T)+f(S)+2f(R)<br /> <br />for all T,S,Rin K(H).