Approximation of derivations and the superstability in random Banach ∗-algebras

Abstract

We prove that approximations of derivations on random Banach * -algebras are exactly derivations by using a fixed point method. Furthermore, we show that approximations of quadratic * -derivations on random Banach * -algebras are exactly quadratic * -derivations. We, moreover, prove that approximations of derivations on random C * -ternary algebras are exactly derivations by using a fixed point method. MSC: 46S50; 47H10; 26E60

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