Achievement of Continuity of (φ, Ψ)-derivations without Linearity
نویسنده
چکیده
Suppose that A is a C∗-algebra acting on a Hilbert space H, and φ, ψ are mappings from A into B(H) which are not assumed to be necessarily linear or continuous. By a (φ, ψ)derivation we mean a linear mapping d : A → B(H) such that d(ab) = φ(a)d(b) + d(a)ψ(b) (a, b ∈ A). In this paper, we prove that if φ is a multiplicative(not necessary linear) ∗-mapping, then every ∗-(φ,φ)-derivation is automatically continuous. Using this fact, we show that every ∗-(φ, ψ)-derivation d from A into B(H) is continuous if and only if the∗-mappings φ and ψ are left and right d-continuous, respectively.
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