UNBOUNDED σ-DERIVATIONS IN C[0-1]

Let A be a C*-algebra, D be a dense subalgebra of A and σ :D→ A be a linear mapping. A linear mapping d:D→ A is called a σ-derivation if d(ab) = d(a) σ (b) + σ (a) d (b) for all a,s Є D. In this paper we characterize all σ-derivations of C[0,1] in terms of the functions d(z), σ(z) and σ(z2), where zn denotes the function t Є [a,b] → tn Є C. we also characterize all linear meppings σ which possesses a σ-derivation d with d(z)(t) ≠ 0 for all t Є [0,1].

Keywords:

Dearivation , closed mapping , closable mapping , (σ , T)-derivation , σ-derivation , vanishing at identity , derivable mapping