Document Type: Research Articles
Department of Mathematics, Semnan University, Semnan, Iran.
Department of Mathematics, Semnan University, Semnan, Iran
Let H be an innite 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-Jensen
type functional equation
2f((T + S)/2+ R) = f(T ) + f(S) + 2f(R)
for all T, S, R are in K(H).