Derivations, homomorphisms, and operator ideals

Abstract

Let A \mathfrak {A} be a C ∗ {C^\ast } -algebra of operators on a Hilbert space, and let C p {C_p} be the Schatten p-ideal. It is shown that every derivation from A \mathfrak {A} to C p {C_p} is inner. A similar argument shows that two C ∗ {C^\ast } -homomorphisms which agree modulo C p {C_p} are equivalent.