Let G be a locally compact abelian group, ω be a weighted function on R + , and let D be the Banach algebra L 0 ∞ ( G ) ∗ or L 0 ∞ ( ω ) ∗ . In this paper, we investigate generalized derivations on the noncommutative Banach algebra D . We characterize k -(skew) centralizing generalized derivations of D and show that the zero map is the only k -skew commuting generalized derivation of D . We also investigate the Singer–Wermer conjecture for generalized derivations of D and prove that the Singer–Wermer conjecture holds for a generalized derivation of D if and only if it is a derivation; or equivalently, it is nilpotent. Finally, we investigate the orthogonality of generalized derivations of L 0 ∞ ( ω ) ∗ and give several necessary and sufficient conditions for orthogonal generalized derivations of L 0 ∞ ( ω ) ∗ .