Derivations mapping into the socle, III

Higher Derivations Associated with the Cauchy-Jensen Type Mapping

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 2f(frac{T+S}{2}+R)=f(T)+f(S)+2f(R) for all T,S,Rin K(H).

Higher Derivations Associated with the Cauchy-Jensen Type Mapping

Let H be an innite 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(...

Derivations Into N-th Duals of Ideals of Banach Algebras

higher derivations associated with the cauchy-jensen type mapping

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 2f(frac{t+s}{2}+r)=f(t)+f(s)+2f(r) for all t,s,rin k(h).

HIGHER POINT DERIVATIONS ON COMMUTATIVE BANACH ALGEBRAS, III fey

i=o hold for each choice of / and g in A and k in { 1 , . . . , q}. A point derivation of infinite order is an infinite sequence {dk} of linear functional such that (1.1) holds for all k. A point derivation is continuous if each dk is continuous, totally discontinuous if dk is discontinuous for each fcSl, and degenerate if d1 = 0. Some of the terminology given in the previous paragraph was intr...